Trigonometry Examples

$4 \sec^{2} (2 π) - 4 = 0$

Step 1

Simplify with factoring out.

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Step 1.1

Factor $4$ out of $4 \sec^{2} (2 π)$ .

$4 (\sec^{2} (2 π)) - 4 = 0$

Step 1.2

Factor $4$ out of $- 4$ .

$4 \sec^{2} (2 π) + 4 \cdot - 1 = 0$

Step 1.3

Factor $4$ out of $4 \sec^{2} (2 π) + 4 \cdot - 1$ .

$4 (\sec^{2} (2 π) - 1) = 0$

Step 2

Apply pythagorean identity.

$4 \tan^{2} (2 π) = 0$

Step 3

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$4 \tan^{2} (0) = 0$

Step 4

The exact value of $\tan (0)$ is $0$ .

$4 \cdot 0^{2} = 0$

Step 5

Raising $0$ to any positive power yields $0$ .

$4 \cdot 0 = 0$

Step 6

Multiply $4$ by $0$ .

$0 = 0$

Step 7