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

✓

Answer

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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