Question

Give answer of question as fast as possible

sin^3x  cos^3x

Answer 1

To solve this problem let's multiply (sin x - cos x) and (1 + sin x* cos x).

(sin x - cos x)*(1 + sin x*cos x)

= sin x + (sin x)^2 * cos x - cos x - sin x * (cos x )^2

Now (sin x)^2 + (cos x)^2 = 1 or (sin x)^2 = 1- (cos x)^2 and (cos x)^2 = 1 - (sin x)^2.

So sin x + (sin x)^2 * cos x - cos x - sin x * (cos x )^2

= sin x + [1- (cos x)^2] * cos x - cos x - sin x *[ 1 - (sin x)^2]

= sin x + cos x - (cos x)^3 - cos x - sin x + ( sin x)^3

subtracting common terms

= ( sin x)^3 - (cos x)^3

Therefore sin^3 x - cos^3 x = (sin x - cos x)(1 + sin x*cos x)

Answer 2

HEY!!

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