Verify: \sec^2x+\tan^2x=(1-\sin^4x)\sec^4x

Dania Robbins

Dania Robbins

Answered question

2022-04-21

Verify:
sec2x+tan2x=(1sin4x)sec4x

Answer & Explanation

alastrimsmnr

alastrimsmnr

Beginner2022-04-22Added 18 answers

My solution:
sec2x+tan2x=1cos2x+sin2xcos2x
=1+sin2xcos2x
=1+sin2xcos2x1sin2x1sin2x
=1sin4xcos2xcos2x
=1cos4xsin4xcos4x
=sec4xsin4xsec4x
=sec4x(1sin4x)

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