sin7θ-sin5θ÷cos7θ+cos5θ=
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(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)
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)
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