Question

Solve for this trig identity step by step.

Answer 1

Using trigonometric identities, and equality is reached, hence the equality is proved.

Which trigonometric identity are used to solve this question?

These three identities are used:

• $\sin^2{x} + \cos^2{x} = 1 \rightarrow \cos^2{x} = 1 - \sin^2{x}$.

• $\sec^2{x} = 1 + \tan^2{x}$.

• $\sec^2{x} = \frac{1}{\cos^2{x}}$

Hence:

$\sec^4{x} = \frac{1 + \tan^2{x}}{1 - \sin^2{x}}$

$\sec^4{x} = \frac{\sec^2{x}}{\cos^2{x}}$

$\sec^4{x} = \sec^2{x} \times \sec^2{x}$

$\sec^4{x} = \sec^4{x}$

Equality is reached, hence the equality is proved.

More can be learned about trigonometric identities at brainly.com/question/24496175

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