A statement of Assertion (A) is followed by a statement of Reason (R). Assertion (A): Maximum value of $\left(\cos^{-1}x\right)^{2}$ is $\pi^{2}$. Reason (R): Range of the principal value branch of $\cos^{-1}x$ is $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]$.

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

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

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

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

CBSE Class 12 · 2023 · Inverse Trigonometric FunctionsMultiple Choice

A statement of Assertion (A) is followed by a statement of Reason (R).
Assertion (A): Maximum value of

(cos^{- 1} x)^{2}

π^{2}

.
Reason (R): Range of the principal value branch of

cos^{- 1} x

[- \frac{π}{2}, \frac{π}{2}]

Answer: (C)

The principal value branch of

cos^{- 1}

has range

[0, π]

, not

[- \frac{π}{2}, \frac{π}{2}]

, so Reason (R) is false.
Since

cos^{- 1} x \in [0, π]

(cos^{- 1} x)^{2} \in [0, π^{2}]

, with maximum

π^{2}

attained at

x = - 1

. So Assertion (A) is true.
Assertion true, Reason false

\Rightarrow

option (C).

(C)

CBSE Class 12 Board · 2023 · Single correct option