Question

The value of sinx + sin3x + sin5x/cosx + cos3x + cos5x is equal to

Answer 1

sin x+sin 3x+sin 5x)/(cos x+cos 3x+cos 5x)=
(sin x + sin 5x) + sin 3x / (cos x + cos 5x) + cos 3x 

= 2sin (x+5x/2)cos (x-5x/2) + sin 3x/ 2cos (x+5x/2)cos (x-5x/2) +cos 3x

=2sin3x cos(-2x) + sin 3x/ 2cos3x cos(-2x) +cos 3x

=2 sin3x(cos 2x) / 2 cos 3x(cos 2x)       
  [as cos 2x and 2 are common on both numerator and dinominator]

 

=sin 3x/ cos 3x =tan 3x.

hope this helps you!!!

Answer 2

Answer:

RHS = ( sin x + sin 3x + sin 5x ) / ( cos x + cos 3x + cos 5x )

        = [ ( sin 5x + sin x ) + sin 3x ] / [ ( cos 5x + cos x ) + cos 3x ]

        = [ ( 2 sin 3x cos x ) + sin 3x ] / [ ( 2 cos 3x cos x ) + cos 3x ]

        = [ sin 3x ( 2 cos x + 1 ) ] / [ cos 3x ( 2 cos x + 1 ) ]

        = sin 3x / cos 3x

        = tan 3x

        = LHS

EASY ANSWER WITH ALL STEPS.