Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite $\csc (x)$ in terms of sines and cosines.

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

Step 1.2

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (x)}$ .

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

Step 1.3

Simplify.

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Step 1.3.1

Raise $\sin (x)$ to the power of $1$ .

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

Step 1.3.2

Raise $\sin (x)$ to the power of $1$ .

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

Step 1.3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.3.4

Add $1$ and $1$ .

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

Step 2

Apply pythagorean identity.

$1$