Question

asin ^3x + bcos^3x = sinxcosx
Then find a^2 + b^2 when asinx = bcosx

Answer 1

Answer:

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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