How do you evaluate $tan(cos^-1(-2/3))$ without a calculator?

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Answer 1 · 2016-08-21T05:56:08

$-sqrt 5/2$

Let $a = cos&(-1)(-2/3) in Q2$ .

Tangent is negative in Q2, and sine is positive..

Now, $cos a =-2/3$ and, the given expression is

$tan a = sin a/cos a.=sqrt(1-cos^2a)/cos a$

$=sqrt(1-(-2/3)^2)/(-2/3)$

$=-sqrt 5/2$

How do you evaluate tan(cos^-1(-2/3))tan(cos^-1(-2/3)) without a calculator?