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Question -

cosec x (sec x – 1) – cot x (1 – cos x) = tan x – sin x



Answer -

Let us consider LHS: cosec x (sec x – 1) – cot x (1 – cos x)
By using the formulas
cosec θ = 1/sin θ;
sec θ = 1/cos θ;
tan θ = sin θ / cos θ;
cot θ = cos θ / sin θ
Now,

By using the formula, 1 – cos2x = sin2x;

= RHS

∴ LHS = RHS

Hence Proved.


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