Description
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)
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Explanation & Answer
1. tan(arctan(9)) =9
2. sin−1(sin(7π/3)) = 7 pi /3
Simplify the expression
3. sin(tan−1x) = x/sqrt(1+x2) ;sin theta = tan theta/sec theta = tan theta/sqrt(1+tan2 theta)
4. tan(sin−1x)= x/sqrt(1-x2) ;tan theta = sin theta/cos theta
5. cos(2 tan−1x) = (1-x2)/(1+x2) ;cos 2 theta = (1-tan2 theta)/(1+tan 2 theta)
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