Question

.
cos x + cos 2 x + cos 3 x / sin x_ sin 2 x + sin 3 x
= cot 2 x​

Answer 1

Step-by-step explanation:

cos x + cos 2x + cos 3x / sin x + sin 2x + sin 3x

= (cosx + cos 3x) + cos 2x / (sinx + sin3x) + sin 2x

=( 2 cos2x cosx )+ cos 2x /( 2 sin 2x cos x ) + sin 2x

( As cos a + cos b = 2 cos (a+b)/2 cos (a-b)/2

and sin a + sin b = 2 sin (a+b)/2 cos (a-b)/2 )

= cos 2x ( 2 cosx +1 )/ sin 2x ( 2 cosx + 1 )

= cos 2x / sin 2x

= cot 2x

I hope this will help you!!