Evaluate the expression

1. tan(arctan(9))

2. sin^{−1}(sin(7π/3))

Simplify the expression

3. sin(tan^{−1} x)

4. tan(sin^{−1} x)

5. cos(2 tan^{−1} x)

1. tan(arctan(9)) =9

2. sin^{−1}(sin(7π/3)) = 7 pi /3

3. sin(tan^{−1}x) = x/sqrt(1+x^{2}) ;sin theta = tan theta/sec theta = tan theta/sqrt(1+tan^{2 } theta)

4. tan(sin^{−1}x)= x/sqrt(1-x^{2}) ;tan theta = sin theta/cos theta

5. cos(2 tan^{−1}x) = (1-x^{2})/(1+x^{2}) ;cos 2 theta = (1-tan^{2} theta)/(1+tan ^{2 } theta)

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