Question

sin (24x)
Show that cos x. cos 2x. cos 4x. cos 8 x =
if sin x 20.
24 sin x​

Answer 1

Answer:

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

multiplying and dividing by 2

2

1

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

=

2

1

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

multiplying and dividing by 2

=

4

1

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

=

4

1

∫ ( sin 4x cos 4x cos 8x cos 16x)dx

multiplying and dividing by 8

=

32

1

∫ (8 sin 4x cos 4x cos 8x cos 16x)dx

=

32

1

∫ (4 sin 8x cos 8x cos 16x)dx

=

32

1

∫ 2 sin 16x cos 16x dx

=

32

1

∫ sin 32x dx

=

32

1

×

32

(−cos32x)

+C

=

1024

−cos32+

+C

Step-by-step explanation:

thank you