How do you solve $csc[tan^-1 (-2)]$ ?

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Answer 1 · 2016-12-03T04:55:16

$csc(tan^(-1)(-2))=-sqrt5/2$

From the definition of inverse ratios, if $tan^(-1)(-2)=theta$ , then $tantheta=-2$

As $tantheta=-2$ , we have $cottheta=-1/2$ and

$csctheta=-sqrt(1+(-1/2)^2)=-sqrt(1+1/4)$

= $-sqrt(5/4)=-sqrt5/2$

Note that as $tantheta$ is negative so would be $csctheta$ as domain for $theta$ is $[-pi/2,pi/2]$ .

hence $csctheta=csc(tan^(-1)(-2))=-sqrt5/2$

How do you solve csc[tan^-1 (-2)] csc[tan^-1 (-2)] ?