asin ^3x + bcos^3x = sinxcosx
Then find a^2 + b^2 when asinx = bcosx
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given asinx = bcosx ........(1)
asin^3x + bcos^3x = sinx.cosx
asinx sin^2x+bcos^3x=sinxcosx
bcosx sin^2x+bcos^3x=sinxcosx
bcosx(sin^2x+cos^2x) = sinx.cosx
bcosx.1 = sinx.cosx then
b = sinx
sinx = b substitue this in (1)
a.b = b cosx then
cosx = asubstitute sinx = b and cosx = a in
asin^3x+bcos^3x = sinx.cosx
a.b^3 + b.a^3 = a.b
ab(a^2+b^2) = ab thus
a^2+b^2 = 1
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