8. in parts (a) to (e) simplify the given expression. In parts (f) to (i) prove the given identity. cot 0 (a) csc 0 – sin 0 -1 sin x sin x (b) 1 + cos x COs x – 1 sin(t) (c) tan (t) + cos(t) 1+ cot2 (x) 1+ tan? (x) (d) cot x 1 — csc х (e) cot x 1 + cos x - Csc x COS x (f) -4 cot x cSc x 1 - cos x 1+ cos x tan? x (g) 1+ cos x sec x – 1 COS x (h) (sin x + cos x)² = 1+ sin(2x) 2(tan x – cot x (i) tan? x – cot2 sin(2æ) 8. (a) sec(0) 1' (b) ; sin(x) (c) tan(t) sec? (t) (d) cot (x) cot (x) 2 (e)

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