Question

if a sin³ x + b cos³ x =sin x.cosx and a sinx=b cos x, then find a²+b²​

Answer 1

Answer:

asin3x+bcos3x=sinx cosx

Substituting asinx=bcosx, we get

asin3x+b cos3x=sinx cosxb cosx sin2x+bcos3x=sinx cosxbcosx  (sin2x+cos2x)=sinx cosx

Solving this we get 

b=sinx and a=cosx

Hence,

a2+b2=sin2x+cos2x=1

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