Question

The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to ______.

पर्याय

• –4

• 0

• –1

• 4

Answer 1

The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to 0.

Explanation:

`"cosec" [sin^-1(-1/2)] - sec [cos^-1((-1)/2)]`

= `"cosec" [-sin^-1(1/2)] - sec [π - cos^-1((-1)/2)]`

= `"cosec" [- π/6] - sec [π - π/3]`

= `-"cosec" [π/6] - sec [(2π)/3]`

= – cosec 30° – sec 120°

= – cosec 30° – sec [(90° + 30°)]

= – 2 – [– cosec 30°]

= – 2 + cosec 30°

= – 2 + 2

= 0