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Question -

Evaluate:

(i) Cot (sin-1 (3/4) + sec-1 (4/3))

(ii) Sin (tan-1 x + tan-1 1/x) for x <0

(iii) Sin (tan-1 x + tan-1 1/x) for x> 0

(iv) Cot (tan-1 a + cot-1 a)

(v) Cos (sec-1 x + cosec-1 x), |x| ≥ 1



Answer -

(i) Given Cot (sin-1 (3/4)+ sec-1 (4/3))

(ii) Given Sin (tan-1 x+ tan-1 1/x) for x < 0

(iii) Given Sin (tan-1 x+ tan-1 1/x) for x > 0

(iv) Given Cot (tan-1 a+ cot-1 a)

(v) Given Cos (sec-1 x+ cosec-1 x), |x| ≥ 1

= 0

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