Trigonometry Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

Add $1$ and $1$ .

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

Step 2

Apply pythagorean identity.

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

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