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:
- [tex]\sin^2{x} + \cos^2{x} = 1 \rightarrow \cos^2{x} = 1 - \sin^2{x}[/tex].
- [tex]\sec^2{x} = 1 + \tan^2{x}[/tex].
- [tex]\sec^2{x} = \frac{1}{\cos^2{x}}[/tex]
Hence:
[tex]\sec^4{x} = \frac{1 + \tan^2{x}}{1 - \sin^2{x}}[/tex]
[tex]\sec^4{x} = \frac{\sec^2{x}}{\cos^2{x}}[/tex]
[tex]\sec^4{x} = \sec^2{x} \times \sec^2{x}[/tex]
[tex]\sec^4{x} = \sec^4{x}[/tex]
Equality is reached, hence the equality is proved.
More can be learned about trigonometric identities at https://brainly.com/question/24496175
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