Evaluate or simplify the expressions

Calculus
Tutor: None Selected Time limit: 1 Day

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)

Feb 23rd, 2015

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)


Feb 23rd, 2015

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