Question

sin7θ-sin5θ÷cos7θ+cos5θ=

Answer 1

(cos 7x + cos 5x ) / (sin 7x - sin 5x)

By using the trigonometric formula,

cos C + cos D = 2 cos (C+D)/2 * cos(C-D)/2

And,

sin C - sin D = 2 cos(C+D)/2 * sin(C-D)/2

We get,

= 2 cos 6x * cos x / 2 cos 6x * sin x

= Cos x / sin x

= Cot x

On differention,

= - cosec^2 x (ans)