How do you evaluate $csc (arctan (- \frac{1}{\sqrt{3}}))$ $csc (arctan(-1 / sqrt3))$ ?

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Answer 1 · 2016-08-05T07:13:42

$- 2$ $-2$

Let $a = a r c tan (- \frac{1}{\sqrt{3}}) \in Q_{4}$ $a = arc tan (-1/sqrt 3) in Q_4$ , wherein sine is negative.

Then, $tan a = - \frac{1}{\sqrt{3}} and sin a = - \frac{1}{2}$ $tan a = -1/sqrt 3 and sin a = -1/2$ .

The given expression is $csc a = \frac{1}{sin a} = - 2$ $csc a = 1/sin a = -2$ ..

How do you evaluate csc(arctan(−1√3))csc (arctan(-1 / sqrt3))?