Question

`sin^2(sin^-1  1/2) + tan^2 (sec^-1  2) + cot^2(cosec^-1  4)` = ______.

Options

• `73/4`

• `37/2`

• `89/4`

• 19

Answer 1

`sin^2(sin^-1  1/2) + tan^2 (sec^-1  2) + cot^2(cosec^-1  4) = underline(73/4)`.

Explanation:

Let cosec^-1 4 = θ ⇒ cosec θ = 4

cot² θ = cosec² θ - 1 = (4)² - 1 = 15

`sin^2(sin^-1  1/2) + tan^2 (sec^-1  2) + cot^2(cosec^-1  4)`

`= sin^2 30^circ + tan^2 60^circ + cot^2 theta`

`= (1/2)^2 + (sqrt3)^2 + 15`

`= 73/4`