Prakalkulus Contoh

$\frac{{(\sin (x) + \tan (x))}^{2} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1

Sederhanakan pembilangnya.

Ketuk untuk lebih banyak langkah...

Langkah 1.1

Tulis kembali $\tan (x)$ dalam bentuk sinus dan kosinus.

$\frac{{(\sin (x) + \frac{\sin (x)}{\cos (x)})}^{2} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.2

Tulis kembali ${(\sin (x) + \frac{\sin (x)}{\cos (x)})}^{2}$ sebagai $(\sin (x) + \frac{\sin (x)}{\cos (x)}) (\sin (x) + \frac{\sin (x)}{\cos (x)})$ .

$\frac{(\sin (x) + \frac{\sin (x)}{\cos (x)}) (\sin (x) + \frac{\sin (x)}{\cos (x)}) + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.3

Perluas $(\sin (x) + \frac{\sin (x)}{\cos (x)}) (\sin (x) + \frac{\sin (x)}{\cos (x)})$ menggunakan Metode FOIL.

Ketuk untuk lebih banyak langkah...

Langkah 1.3.1

Terapkan sifat distributif.

$\frac{\sin (x) (\sin (x) + \frac{\sin (x)}{\cos (x)}) + \frac{\sin (x)}{\cos (x)} (\sin (x) + \frac{\sin (x)}{\cos (x)}) + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.3.2

Terapkan sifat distributif.

$\frac{\sin (x) \sin (x) + \sin (x) \frac{\sin (x)}{\cos (x)} + \frac{\sin (x)}{\cos (x)} (\sin (x) + \frac{\sin (x)}{\cos (x)}) + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.3.3

Terapkan sifat distributif.

$\frac{\sin (x) \sin (x) + \sin (x) \frac{\sin (x)}{\cos (x)} + \frac{\sin (x)}{\cos (x)} \sin (x) + \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4

Sederhanakan dan gabungkan suku-suku sejenis.

Ketuk untuk lebih banyak langkah...

Langkah 1.4.1

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 1.4.1.1

Kalikan $\sin (x) \sin (x)$ .

Ketuk untuk lebih banyak langkah...

Langkah 1.4.1.1.1

Naikkan $\sin (x)$ menjadi pangkat $1$ .

$\frac{\sin^{1} (x) \sin (x) + \sin (x) \frac{\sin (x)}{\cos (x)} + \frac{\sin (x)}{\cos (x)} \sin (x) + \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.1.2

Naikkan $\sin (x)$ menjadi pangkat $1$ .

$\frac{\sin^{1} (x) \sin^{1} (x) + \sin (x) \frac{\sin (x)}{\cos (x)} + \frac{\sin (x)}{\cos (x)} \sin (x) + \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.1.3

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$\frac{{\sin (x)}^{1 + 1} + \sin (x) \frac{\sin (x)}{\cos (x)} + \frac{\sin (x)}{\cos (x)} \sin (x) + \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.1.4

Tambahkan $1$ dan $1$ .

$\frac{\sin^{2} (x) + \sin (x) \frac{\sin (x)}{\cos (x)} + \frac{\sin (x)}{\cos (x)} \sin (x) + \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.2

Kalikan $\sin (x) \frac{\sin (x)}{\cos (x)}$ .

Ketuk untuk lebih banyak langkah...

Langkah 1.4.1.2.1

Gabungkan $\sin (x)$ dan $\frac{\sin (x)}{\cos (x)}$ .

$\frac{\sin^{2} (x) + \frac{\sin (x) \sin (x)}{\cos (x)} + \frac{\sin (x)}{\cos (x)} \sin (x) + \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.2.2

Naikkan $\sin (x)$ menjadi pangkat $1$ .

$\frac{\sin^{2} (x) + \frac{\sin^{1} (x) \sin (x)}{\cos (x)} + \frac{\sin (x)}{\cos (x)} \sin (x) + \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.2.3

Naikkan $\sin (x)$ menjadi pangkat $1$ .

$\frac{\sin^{2} (x) + \frac{\sin^{1} (x) \sin^{1} (x)}{\cos (x)} + \frac{\sin (x)}{\cos (x)} \sin (x) + \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.2.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$\frac{\sin^{2} (x) + \frac{{\sin (x)}^{1 + 1}}{\cos (x)} + \frac{\sin (x)}{\cos (x)} \sin (x) + \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.2.5

Tambahkan $1$ dan $1$ .

$\frac{\sin^{2} (x) + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin (x)}{\cos (x)} \sin (x) + \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.3

Kalikan $\frac{\sin (x)}{\cos (x)} \sin (x)$ .

Ketuk untuk lebih banyak langkah...

Langkah 1.4.1.3.1

Gabungkan $\frac{\sin (x)}{\cos (x)}$ dan $\sin (x)$ .

$\frac{\sin^{2} (x) + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin (x) \sin (x)}{\cos (x)} + \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.3.2

Naikkan $\sin (x)$ menjadi pangkat $1$ .

$\frac{\sin^{2} (x) + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{1} (x) \sin (x)}{\cos (x)} + \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.3.3

Naikkan $\sin (x)$ menjadi pangkat $1$ .

$\frac{\sin^{2} (x) + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{1} (x) \sin^{1} (x)}{\cos (x)} + \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.3.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$\frac{\sin^{2} (x) + \frac{\sin^{2} (x)}{\cos (x)} + \frac{{\sin (x)}^{1 + 1}}{\cos (x)} + \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.3.5

Tambahkan $1$ dan $1$ .

$\frac{\sin^{2} (x) + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.4

Kalikan $\frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)}$ .

Ketuk untuk lebih banyak langkah...

Langkah 1.4.1.4.1

Kalikan $\frac{\sin (x)}{\cos (x)}$ dengan $\frac{\sin (x)}{\cos (x)}$ .

$\frac{\sin^{2} (x) + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin (x) \sin (x)}{\cos (x) \cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.4.2

Naikkan $\sin (x)$ menjadi pangkat $1$ .

$\frac{\sin^{2} (x) + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{1} (x) \sin (x)}{\cos (x) \cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.4.3

Naikkan $\sin (x)$ menjadi pangkat $1$ .

$\frac{\sin^{2} (x) + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{1} (x) \sin^{1} (x)}{\cos (x) \cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.4.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$\frac{\sin^{2} (x) + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos (x)} + \frac{{\sin (x)}^{1 + 1}}{\cos (x) \cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.4.5

Tambahkan $1$ dan $1$ .

$\frac{\sin^{2} (x) + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos (x) \cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.4.6

Naikkan $\cos (x)$ menjadi pangkat $1$ .

$\frac{\sin^{2} (x) + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos^{1} (x) \cos (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.4.7

Naikkan $\cos (x)$ menjadi pangkat $1$ .

$\frac{\sin^{2} (x) + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos^{1} (x) \cos^{1} (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.4.8

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$\frac{\sin^{2} (x) + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{{\cos (x)}^{1 + 1}} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.1.4.9

Tambahkan $1$ dan $1$ .

$\frac{\sin^{2} (x) + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos^{2} (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.4.2

Tambahkan $\frac{\sin^{2} (x)}{\cos (x)}$ dan $\frac{\sin^{2} (x)}{\cos (x)}$ .

$\frac{\sin^{2} (x) + 2 \frac{\sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos^{2} (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.5

Gabungkan $2$ dan $\frac{\sin^{2} (x)}{\cos (x)}$ .

$\frac{\sin^{2} (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos^{2} (x)} + \cos^{2} (x) - \sec^{2} (x)}{\tan (x)}$

Langkah 1.6

Tulis kembali $\sec (x)$ dalam bentuk sinus dan kosinus.

$\frac{\sin^{2} (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos^{2} (x)} + \cos^{2} (x) - {(\frac{1}{\cos (x)})}^{2}}{\tan (x)}$

Langkah 1.7

Terapkan kaidah hasil kali ke $\frac{1}{\cos (x)}$ .

$\frac{\sin^{2} (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos^{2} (x)} + \cos^{2} (x) - \frac{1^{2}}{\cos^{2} (x)}}{\tan (x)}$

Langkah 1.8

Satu dipangkat berapa pun sama dengan satu.

$\frac{\sin^{2} (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos^{2} (x)} + \cos^{2} (x) - \frac{1}{\cos^{2} (x)}}{\tan (x)}$

Langkah 1.9

Tulis kembali $\sin^{2} (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{2} (x)}{\cos^{2} (x)} + \cos^{2} (x) - \frac{1}{\cos^{2} (x)}$ dalam bentuk faktor.

Ketuk untuk lebih banyak langkah...

Langkah 1.9.1

Biarkan $u = \frac{2 \sin^{2} (x)}{\cos (x)}$ . Masukkan $u$ untuk semua kejadian $\frac{2 \sin^{2} (x)}{\cos (x)}$ .

Ketuk untuk lebih banyak langkah...

Langkah 1.9.1.1

Kurangi $1$ dengan $1$ .

$\frac{u + 0}{\tan (x)}$

Langkah 1.9.1.2

Tambahkan $u$ dan $0$ .

$\frac{u}{\tan (x)}$

Langkah 1.9.2

Ganti semua kemunculan $u$ dengan $\frac{2 \sin^{2} (x)}{\cos (x)}$ .

$\frac{\frac{2 \sin^{2} (x)}{\cos (x)}}{\tan (x)}$

Langkah 2

Tulis kembali $\tan (x)$ dalam bentuk sinus dan kosinus.

$\frac{\frac{2 \sin^{2} (x)}{\cos (x)}}{\frac{\sin (x)}{\cos (x)}}$

Langkah 3

Kalikan pembilang dengan balikan dari penyebut.

$\frac{2 \sin^{2} (x)}{\cos (x)} \cdot \frac{\cos (x)}{\sin (x)}$

Langkah 4

Gabungkan.

$\frac{2 \sin^{2} (x) \cos (x)}{\cos (x) \sin (x)}$

Langkah 5

Hapus faktor persekutuan dari $\sin^{2} (x)$ dan $\sin (x)$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.1

Faktorkan $\sin (x)$ dari $2 \sin^{2} (x) \cos (x)$ .

$\frac{\sin (x) (2 \sin (x) \cos (x))}{\cos (x) \sin (x)}$

Langkah 5.2

Batalkan faktor persekutuan.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.1

Faktorkan $\sin (x)$ dari $\cos (x) \sin (x)$ .

$\frac{\sin (x) (2 \sin (x) \cos (x))}{\sin (x) \cos (x)}$

Langkah 5.2.2

Batalkan faktor persekutuan.

$\frac{\sin (x) (2 \sin (x) \cos (x))}{\sin (x) \cos (x)}$

Langkah 5.2.3

Tulis kembali pernyataannya.

$\frac{2 \sin (x) \cos (x)}{\cos (x)}$

Langkah 6

Batalkan faktor persekutuan dari $\cos (x)$ .

Ketuk untuk lebih banyak langkah...

Langkah 6.1

Batalkan faktor persekutuan.

$\frac{2 \sin (x) \cos (x)}{\cos (x)}$

Langkah 6.2

Bagilah $2 \sin (x)$ dengan $1$ .

$2 \sin (x)$