Question

Please help me to prove this and get 50 points. No spamming please:
$\frac{cos2x \: sinx \: + \: cos 6x \: sin 3x}{sin2x \: sinx \: + \: sin6x \: sin 3x} = cot5x$
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Answer 1

Step-by-step explanation:

This is your answer friends

Answer 2

Step-by-step explanation:

solve this problem, we can use the identities:

sinA+sinB=2sinA+B2cosA−B2,

cosA+cosB=2cosA+B2cosA−B2,

and

sin2ϕ=2sinϕcosϕ.

Going back to the question,

LHS=sin2x+sin4x+sin6x=2sin3xcosx+sin6x=2sin3xcosx+2sin3xcos3x=2sin3x(cosx+cos3x)=2sin3x×2cos2xcosx=4cosxcos2xsin3x=RHS.

Hence, proved.