Question

What is sin inverse x + sin inverse y formula?

Answer 1

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Answer 2

The trigonometric function of an inverse is found out by a right-angled triangle of length 1 and another side of length x.  By using the Pythagorean theorem, it is obtained that the formula for $Sin^{-1} x + Sin^{-1}y$ is given as follows

$Sin^{-1} x + Sin^{-1}y = Sin^{-1}[x \sqrt{1 - y^2} + y\sqrt{1 - x^2}]$  

Similarly, we can write it as,

$Sin^{-1}x - Sin^{-1}y = Sin-1[x\sqrt{1 - y^2}- y\sqrt{1 - x^2}]$