Question

please give me the answer and steps of this integration Integal sin 6 x + cos 6 x / sin 2 x cos 2x dx ?

Answer 1

sin 6x + cos6x = 2sin6xcos6x
=sin12x

sin2xcos2x=(sin4x)/2

sin 6 x + cos 6 x / sin 2 x cos 2x = 2(sin12x / sin4x)
4x = A
2 (sin3A/sinA)
2 (3sinA - 4sin*3A)/sinA
2 (3 - 4sin*2A)
2 (1 + 2(1 - 2sin*2A)
2 (1 + 2cos2A)
2 + 4cos8x

integral (sin 6 x + cos 6 x / sin 2 x cos 2x)
= integral (2 + 4 cos8x)
= 2x + (4sin8x)/8
= 2x + (sin8x)/2