Convert (i) `tan^(-1)3,` (ii) `sin^(-1)(-1//3)` in terms of cosine inverse.

The value of tan[sin^(-1) (3/5)+tan^(-1) (2/3)] is

Define: tan^(-1)((3x-x^(3))/(1-3x^(2))) in terms of tan^(-1)x

Define: tan^(-1)((3x-x^(3))/(1-3x^(2))) in terms of tan^(-1)x

Find the principal value of: i) sin^(-1)(sqrt(3)/2) ii) sin^(-1)(1/2) iii) cos^(-1)(1/2) iv) tan^(-1)(1) v) tan^(-1)(1/sqrt(3)) vi) sec^(-1)(2/sqrt(3)) , vii) "cosec"^(-1)(sqrt(2)) .

Evaluate: i) sin(cos^(-1)(3/5)) , ii) cos(tan^(-1)(3/4))

Evaluate each of the following: tan(tan^(-1)3/4) (ii) tan(sin^(-1)5/(13)) (iii) tan(cos^(-1)8/(17))

Evaluate: (i) sin{cos^(-1)(-3/5)} (ii) tan{cos^(-1)(-(12)/(13))}

Simplify (i) sin(pitan{cot^(-1)((-2)/3)}) (ii) sin(2"tan"^(-1)1/2) (iii) cos(2cos^(-1)(1//5)+sin^(-1)(1//5))

Simplify (i) sin(pitan{cot^(-1)((-2)/3)}) (ii) sin(2"tan"^(-1)1/2) (iii) cos(2cos^(-1)(1//5)+sin^(-1)(1//5))

If x=sin(2tan^(-1)3)and y=sin((1)/(2)tan^(-1)(4/3)) , then