Trigonometry Examples

$1 - \sin^{2} (x) = \sin (x) \cos (x) \cot (x)$

Step 1

Apply pythagorean identity.

$\cos^{2} (x) = \sin (x) \cos (x) \cot (x)$

Step 2

Simplify $\sin (x) \cos (x) \cot (x)$ .

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

Factor $\sin (x)$ out of $\sin (x) \cos (x)$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

$\cos^{2} (x) = \cos (x) \cos (x)$

Step 2.3

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

$\cos^{2} (x) = \cos^{1} (x) \cos (x)$

Step 2.4

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

$\cos^{2} (x) = \cos^{1} (x) \cos^{1} (x)$

Step 2.5

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

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

Step 2.6

Add $1$ and $1$ .

$\cos^{2} (x) = \cos^{2} (x)$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 0, - 0.1, 0.1, \frac{1}{5}, 0.3, \frac{2}{5}, - \frac{1}{2}$

Step 4