Question

`(tan^-1 (sqrt(3)) - sec^-1(-2))/("cosec"^-1(-sqrt(2)) + cos^-1(-1/2))` is equal to ______.

Options

• `4/5`

• `-4/5`

• `3/5`

• 0

Answer 1

`(tan^-1 (sqrt(3)) - sec^-1(-2))/("cosec"^-1(-sqrt(2)) + cos^-1(-1/2))` is equal to `underlinebb(-4/5)`.

Explanation:

`(tan^-1 (sqrt(3)) - sec^-1(-2))/("cosec"^-1(-sqrt(2)) + cos^-1(-1/2))` 

= `(tan^-1(sqrt(3)) - (π - sec^-1 (2)))/(-"cosec"^-1 (sqrt(2)) + π - cos^-1(1/2))`

= `(π/3 - (π - π/3))/(-π/4 + π - π/3)`

= `(-π/3)/((12π - 3π - 4π)/12)`

= `(-π/3)/((5π)/12)`

= `-4/5`