Prove that 1-tan^2x/1+tan^2x = cos2x is an identity?

Maxim Rosales

Maxim Rosales

Answered question

2023-01-01

Prove that 1tan2x1+tan2x=cos2x is an identity?

Answer & Explanation

dejalacorrer9kv

dejalacorrer9kv

Beginner2023-01-02Added 7 answers

So we have: 1tan2x1+tan2x
=1sin2xcos2x1+sin2xcos2x
=cos2xsin2xcos2xcos2x+sin2xcos2x
=cos2xsin2xcos2x+sin2x
=cos2xsin2x
=cos2x
Everett Douglas

Everett Douglas

Beginner2023-01-03Added 2 answers

As we known:
RHS=cos2x
=cos(x+x)
=cosxcosxsinxsinx
=cos2xsin2x
=cos2xsin2xcos2x+sin2x
=cos2xcos2xsin2xcos2xcos2xcos2x+sin2xcos2x
=1tan2x1+tan2x=LHS

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