Prove that :sin2x+2sin4x+sin6x=4cos^2xsin4x

Kymani Estrada

Kymani Estrada

Answered question

2023-01-06

Prove that :sin2x+2sin4x+sin6x=4cos2xsin4x

Answer & Explanation

Ayden Davidson

Ayden Davidson

Beginner2023-01-07Added 10 answers

sin2x+2sin4x+sin6x=4cos2xsin4x
LHS=sin2x+2sin4x+sin6x=(sin6x+sin2x)+2sin4x(i)WeknowsinA+sinB=2sin(A+B)2cos(A-B)2(i)becomes2sin4xcos2x+2sin4x=2sin4x(cos2x+1)=2sin4x(2cos2x1+1)=2sin4x(2cos2x)=4cos2xsin4x=RHS

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