Question

Y=sinx.cosx.cos2x.cos4x.cos8x find dy/dx​

Answer 1

Answer:

∫ (sin x cos x cos 2x cos 4x cos 8x cos 16x)dx

multiplying and dividing by 2

1/2∫ (2 sin x cos x cos 2x cos 4x cos 8x cos 16)dx

1/2 ∫ (sin 2x cos 2x cos 4x cos 8x cos 16x)dx   [∵ 2 sin x cos x = sin 2x]

multiplying and dividing by 2

=1/4 ∫(2 sin 2x cos 2x cos 4x cos 8x cos 16x)dx

=1/4 ∫ ( sin 4x cos 4x cos 8x cos 16x)dx

multiplying and dividing by 8

=1/32 ∫ (8 sin 4x cos 4x cos 8x cos 16x)dx

=1/32 ∫ (4 sin 8x cos 8x cos 16x)dx

=1/32 ∫ 2 sin 16x cos 16x dx

=1/ 32 ∫ sin 32x dx

=1/32*(-cos32x)/32+c

=-cos32x/1024+c(Ans)

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