Question

`(sin^-1(-1/2) + tan^-1(-1/sqrt(3)))/(sec^-1 (-2/sqrt(3)) + cos^-1(1/sqrt(2))` = ______.

Options

• `4/5`

• `(-6)/19`

• `3/19`

• `(-4)/13`

Answer 1

`(sin^-1(-1/2) + tan^-1(-1/sqrt(3)))/(sec^-1 (-2/sqrt(3)) + cos^-1(1/sqrt(2))` = `(-4)/13`.

Explanation:

`(sin^-1(-1/2) + tan^-1(-1/sqrt(3)))/(sec^-1 (-2/sqrt(3)) + cos^-1(1/sqrt(2))) = (- pi/6 - pi/6)/((5pi)/6 + pi/4)` 

= `(-4)/13`