Question

plz solve this question of trigonometry​

Answer 1

Answer:

sin 5x +sin 3x/ cos 5x+ cos 3x

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

sin (8x/2) cos (2x/2)/ cos (8x/2)cos (2x/2)

sin 4x/cos 4x

tan x

Answer 2

sin 5x + sin 3x

=====>

Using sin x + sin y

=

2 sin[(x+y)/2] cos [ (x-y)/2]

Putting x = 5x & y = 3x

2 sin[(5x + 3x)/2] cos[(5x - 3x)/2]

2 sin(8x/2) cos(2x/2)

2 sin 4x cos x (1)

cos 5x + cos 3x

======>

Using cos x +cos y

=

2cos [( x+y)/2] cos[(x-y)/2]

Putting x = 5x & y = 3x

2 cos[(5x +3x)/2] cos[( 5x -3 x)/2]

2 cos(8x/2) cos(2x/2)

2 cos 4x cos x. (2)

Dividing 1 and 2

2 sin 4x cos x/ 2 cos 4x cos x

sin 4x/ cos 4x

=======>

tan 4x. ( sin/cos = tan)

Hence proved