Solve identity : \frac{1+\sin x\cos x}{\cos^3 x - \sin^3 x}+\frac{1}{\sin

komanijuuxw

komanijuuxw

Answered question

2022-04-20

Solve identity : 1+sinxcosxcos3xsin3x+1sinx+cosx+sin2x2cosx1cos2xsin2x=1tan2x1

Answer & Explanation

Alice Harmon

Alice Harmon

Beginner2022-04-21Added 12 answers

Use a3b3=(ab)(a2+ab+b2)
Therefore we have,
cos3xsin3x=(cosxsinx)(1+sinxcosx)
Your expression in LHS
1+sinxcosxcos3xsin3x+1sinx+cosx+sin2x2cosx1cos2xsin2x
Simplifies to
LHS=1cosxsinx+1sinx+cosx+sin2x2cosx1cos2xsin2x
=2cosxcos2xsin2x+sin2x2cosx1cos2xsin2x
=2cosx+sin2x2cosx1cos2xsin2x
=sin2x1cos2xsin2x
=cos2xsin2xcos2x
=1tan2x1=RHS

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