Question

How to prove, cot 4x (sin 5x + sin 3x) = cot x (sin 5x - sin 3x ) ?

Answer 1

these identities might work
sinA + sinB = 2sin1/2(A+B)cos1/2(A-B)
sinA - sinB = 2cos1/2(A+B)sin1/2(A-B)
and cot = cos/sin

Answer 2

Ok Friend, I know these equations. But, how can i prove this?

Answer 3

for LHS :
cot 4x (sin 5x + sin 3x)
= (cot4x/sin4x) (2sin1/2(5x+3x)cos1/2(5x-3x))
= (cot4x/sin4x) (2sin4xcosx)
cancel the sin4x's
= 2cos4xcosx

now, do same idea for the RHS

Answer 4

you have to show that LHS = RHS

Answer 5

:) ok. thank you