How do you solve and find the value of $cot(sin^-1(5/6))$ ?

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Answer 1 · 2017-01-19T14:21:33

$cottheta=+sqrt11/5$ .

Let $sin^-1(5/6)=theta rArr sintheta=5/6, theta in [-pi/2,pi/2]$

But as $sintheta >0, theta in (0,pi/2)$

We require the value= $cottheta$

Knowing that #csc^2theta=1+cot^2theta, we have,

$cot^2theta=csc^2theta-1=1/sin^2theta-1=36/25-1=11/25$

$rArr cottheta=+-sqrt11/5$

As, $theta in (0,pi/2), cottheta=+sqrt11/5$ .

How do you solve and find the value of cot(sin^-1(5/6))cot(sin^-1(5/6))?