Trigonometry Examples

$2 \cos (x) \sec (x) + \cos (x) = 0$

Step 1

Simplify the left side.

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Step 1.1

Simplify each term.

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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

Add parentheses.

$2 (\cos (x) \sec (x)) + \cos (x) = 0$

Step 1.1.1.2

Reorder $\cos (x)$ and $\sec (x)$ .

$2 (\sec (x) \cos (x)) + \cos (x) = 0$

Step 1.1.1.3

Rewrite $2 \cos (x) \sec (x)$ in terms of sines and cosines.

$2 (\frac{1}{\cos (x)} \cos (x)) + \cos (x) = 0$

Step 1.1.1.4

Cancel the common factors.

$2 \cdot 1 + \cos (x) = 0$

Step 1.1.2

Multiply $2$ by $1$ .

$2 + \cos (x) = 0$

Step 2

Subtract $2$ from both sides of the equation.

$\cos (x) = - 2$

Step 3

The range of cosine is $- 1 \leq y \leq 1$ . Since $- 2$ does not fall in this range, there is no solution.

No solution