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" (b) "cot^(-1)(sqrt(1+x^(2))+x)...

" (b) "cot^(-1)(sqrt(1+x^(2))+x)

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cot^(-1)sqrt(x)

cot^(-1)sqrt(x)

Write into the simplest form: cot^(-1)(sqrt(1+x^(2))+x)

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

If -1< x < 0 , then cos^(-1)x is equal to (a) sec^(-1)(1/ x) (b) pi-sin^(-1)sqrt(1+x^2) (c) pi+tan^(-1)(x/(sqrt(1-x^2))) (d) cot^(-1)(x/(sqrt(1-x^2))) .

If -1< x < 0 , then cos^(-1)x is equal to (a) sec^(-1)(1/ x) (b) pi-sin^(-1)sqrt(1+x^2) (c) pi+tan^(-1)(x/(sqrt(1-x^2))) (d) cot^(-1)(x/(sqrt(1-x^2))) .

(d)/(dx)[tan^(-1)sqrt(1+x^(2))-cot^(-1)(-sqrt(1+x^(2)))]=