Question

How do you simplify `(sin6x)/(sin5x)`?

Answer 1

sinx.cot 5x + cos x

Explanation:

Use trig identity: sin (a + b) = sin a.cos b + sin b.cos a
sin 6x = sin (x + 5x) = sin x.cos 5x + sin 5x.cos x
`(sin 6x)/(sin 5x) = (sin x.cos 5x + sin 5x.cos x)/(sin 5x) =`
`= sin x.cot 5x + cos x`