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Question
Prove that:
tan(π + x) cot(x – π) – cos(2π – x) cos(2π + x) = sin2 x.
Solution
tan(π + x) cot(x – π) – cos(2π – x) cos(2π + x) = (tan x) (-cot(π – x) – cos x cos x
[∵ cot(x – π) = cot(-(π – x)) = -cot(π – x) = cot x]
= tan x cot x – cos2 x
= 1 – cos2 x
= sin2 x [∵ sin2 x + cos2 x = 1 ⇒ sin2 x = (1 – cos2 x)]
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