Precalculus Examples

$\sin (θ) (\csc (θ) - \sin (θ))$

Step 1

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

$\sin (θ) (\frac{1}{\sin (θ)} - \sin (θ))$

Step 2

Apply the distributive property.

$\sin (θ) \frac{1}{\sin (θ)} + \sin (θ) (- \sin (θ))$

Step 3

Cancel the common factor of $\sin (θ)$ .

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Step 3.1

Cancel the common factor.

$\sin (θ) \frac{1}{\sin (θ)} + \sin (θ) (- \sin (θ))$

Step 3.2

Rewrite the expression.

$1 + \sin (θ) (- \sin (θ))$

Step 4

Rewrite using the commutative property of multiplication.

$1 - \sin (θ) \sin (θ)$

Step 5

Multiply $- \sin (θ) \sin (θ)$ .

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Step 5.1

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

$1 - (\sin^{1} (θ) \sin (θ))$

Step 5.2

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

$1 - (\sin^{1} (θ) \sin^{1} (θ))$

Step 5.3

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

$1 - {\sin (θ)}^{1 + 1}$

Step 5.4

Add $1$ and $1$ .

$1 - \sin^{2} (θ)$

Step 6

Apply pythagorean identity.

$\cos^{2} (θ)$