Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Assertion (A): Domain of $y=\cos^{-1}(x)$ is $[-1,1]$. Reason (R): The range of the principal value branch of $y=\cos^{-1}(x)$ is $[0,\pi]-\left\{\dfrac{\pi}{2}\right\}$.

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

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

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

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

CBSE Class 12 · 2024 · Inverse Trigonometric FunctionsMultiple Choice

Two statements are given, one labelled Assertion (A) and the other labelled Reason (R).
Assertion (A): Domain of

y = cos^{- 1} (x)

[- 1, 1]

.
Reason (R): The range of the principal value branch of

y = cos^{- 1} (x)

[0, π] - {\frac{π}{2}}

(A)Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
(B)Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of the Assertion (A).
(C)Assertion (A) is true, but Reason (R) is false.✓ Correct
(D)Assertion (A) is false, but Reason (R) is true.

Answer: (C)

The domain of

cos^{- 1}

[- 1, 1]

, so Assertion (A) is true.
The range of the principal value branch of

cos^{- 1}

is the full interval

[0, π]

;

\frac{π}{2}

is not excluded (indeed

cos^{- 1} 0 = \frac{π}{2}

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

\Rightarrow

option (C).

(C)

CBSE Class 12 Board · 2024 · Single correct option