Question

prove that 6(cos^10 x+ sin^10x) - 15(cos^8x + sin^8x) + 10(cos^6x + sin^6x)=1

Answer 1

Answer:

Step-by-step exTo 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, provedplanation: