Trigonometry Examples

$2 + 2 \tan^{2} (x) - 5 \sec (x) = 0$

Step 1

Simplify $2 + 2 \tan^{2} (x) - 5 \sec (x)$ .

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Step 1.1

Factor $2$ out of $2$ .

$2 (1) + 2 \tan^{2} (x) - 5 \sec (x) = 0$

Step 1.2

Factor $2$ out of $2 \tan^{2} (x)$ .

$2 (1) + 2 (\tan^{2} (x)) - 5 \sec (x) = 0$

Step 1.3

Factor $2$ out of $2 (1) + 2 (\tan^{2} (x))$ .

$2 (1 + \tan^{2} (x)) - 5 \sec (x) = 0$

Step 1.4

Rearrange terms.

$2 (\tan^{2} (x) + 1) - 5 \sec (x) = 0$

Step 1.5

Apply pythagorean identity.

$2 \sec^{2} (x) - 5 \sec (x) = 0$

Step 2

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

$x \approx 1.15927948 + 2 π n, 5.12390582 + 2 π n$ , for any integer $n$

Step 3