Trigonometry Examples

$\cos (\tan (x) \cot (x)) = \csc (x)$

Step 1

Simplify the left side.

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Step 1.1

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

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Step 1.1.1

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 1.1.1.1

Reorder $\tan (x)$ and $\cot (x)$ .

$\cos (\cot (x) \tan (x)) = \csc (x)$

Step 1.1.1.2

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

$\cos (\frac{\cos (x)}{\sin (x)} \cdot \frac{\sin (x)}{\cos (x)}) = \csc (x)$

Step 1.1.1.3

Cancel the common factors.

$\cos (1) = \csc (x)$

Step 1.1.2

Evaluate $\cos (1)$ .

$0.5403023 = \csc (x)$

Step 2

Rewrite the equation as $\csc (x) = 0.5403023$ .

$\csc (x) = 0.5403023$

Step 3

The range of cosecant is $y \leq - 1$ and $y \geq 1$ . Since $0.5403023$ does not fall in this range, there is no solution.

No solution