Assertion (A): cosec ^ -1 [ cosec ( 5 6 ) ] = 6 . Reason (R): The principal value range…
Mathematics · Class 12 · CBSE — Inverse Trigonometric Functions
Assertion (A): \(\text{cosec}^{-1}\left[\text{cosec}\left(\frac{5\pi}{6}\right)\right] = \frac{\pi}{6}\).
Reason (R): The principal value range of \(\text{cosec}^{-1} x\) lies in \(\left(-\frac{\pi}{2}, 0\right) \cup \left(0, \frac{\pi}{2}\right)\).
- 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
(C) (A) is true but (R) is false.
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- Prove that ^ -1 ( cosec x x cosec x + x ) = 4 - x 2 where - 2 x 2 .
- Prove: ^ -1 ( 1+ x + 1- x 1+ x - 1- x ) = 4 + x 2 , 0 x 2 .
- The given graph (passing through points (- 1 5 , ) and ( 1 5 , 0 ) with y -axis intercept 2 ) shows:
- Assertion (A): If , are the roots of the equation 6( ^ -1 x)^2 - ^ -1 x - ^2 = 0 , then + = 2 - 3 2 . Reason…
- Prove that ^ -1 ( y b^2 - y^2 ) = ^ -1 ( y b ) , -b y b .
- Find the domain and principal value branch of y = 2 ^ -1 (3x) .
- The value of [ ^ -1 ( ( ^ -1 ( -1 2 ) ) ) ] is:
- Find the principal value of ^ -1 2 3 ( 9 2 ^ -1 1 2 ) .
More Inverse Trigonometric Functions questions · Browse all practice questions