Assertion (A) : All trigonometric functions have their inverses o… - Vidyadip

MCQ

Assertion (A) : All trigonometric functions have their inverses over their respective domains.
Reason (R) : The inverse of $\tan ^{-1} x$ exists for some $x \in R$.

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

✓

Answer

Correct option: D.

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

(d) : All trigonometric functions are periodic and hence not invertible over their respective domains but all trigonometric functions have inverse over their restricted domains.
Inverse of $\tan ^{-1} x$ is $\tan x$ which is defined for
$
x \in R-(2 n+1) \frac{\pi}{2}, n \in Z
$
$\therefore \quad$ Assertion is false and reason is true.

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