Question

Assertion (A): Value of the expression `sin^-1 (sqrt(3)/2) + tan^-1 1 - sec^-1 (sqrt(2))` is `π/4`.

Reason (R): Principal value branch of sin^–1 x is `[-π/2, π/2]` and that of sec^–1 x is `[0, π] - {π/2}`.

पर्याय

• Both (A) and (R) are true and (R) is the correct explanation of (A).

• Both (A) and (R) are true but (R) is not the correct explanation of (A).

• (A) is true but (R) is false.

• (A) is false but (R) is true.

Answer 1

(A) is false but (R) is true.

Explanation:

`sin^-1 (sqrt(3)/2) + tan^-1 1 - sec^-1 (sqrt(2))`

= `π/3 + π/4 - π/4`

= `π/3 ≠ π/4`

So, A is false.

Principal value branch of sin^–1 x is `[-π/2, π/2]` and that of sec^–1 x is `[0, π] - {π/2}`.

So, R is true.