What does 2sin(arccot(5))-3sin(arc csc(2)) equal?

Apr 1, 2016

$\frac{2}{\sqrt{26}} - \frac{3}{2}$

Explanation:

sin arcsin k =k.

If $\cot a = \frac{x}{y} , \sin a = \frac{y}{\sqrt{{x}^{2} + {y}^{2}}}$.

So, $a r c \cot \left(\frac{5}{1}\right) = a r c \sin \left(\frac{1}{\sqrt{26}}\right)$

If $\csc c = d , \sin c = \frac{1}{d}$.

Here x = 5, y = 1, d = 2.
The given expression is
$2 \sin \arcsin \left(\frac{1}{\sqrt{26}}\right) - 3 \sin \arcsin \left(\frac{1}{2}\right)$
= $2 \left(\frac{1}{\sqrt{26}}\right) - 3 \left(\frac{1}{2}\right)$