Solve the equation (cosx+cos3x+cos5x)/(sinx+sin3x+sin5x)=square root of 3.

We have to solve the equation (cos x + cos 3x + cos 5x) /
(sin x + sin 3x + sin 5x) = sqrt 3.

Now we know that cos x
+ cos y= 2cos[x+y)/2]*cos [(x-y)/2]

=>cos x + cos
(5x)= 2 cos[(x+5x)/2]*cos[(x-5x)/2]

=> cos x + cos
(5x)= 2cos(3x)cos(2x)

=> (cos x + cos 3x + cos 5x) =
2cos(3x)cos(2x) + cos 3x

=> cos 3x( 2cos 2x
+1)

sin A + sin B = 2 sin [ (A + B) / 2 ] cos [ (A - B) / 2
]

=> sin x + sin 5x = 2 sin 3x * cos
2x

sin x + sin3x + sin5x = 2 sin 3x * cos 2x + sin
3x

= sin 3x( 2cos 2x + 1)

cos
3x( 2cos 2x +1)/ sin 3x( 2cos 2x + 1)

= 1/ tan 3x = sqrt
3

tan 3x = 1/ sqrt 3

3x = arc
tan (1/ sqrt 3)

=> 3x = 30
degrees

=> x=  10
degrees.

Therefore x = 10
degrees.