JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
Let \(\alpha = 3\sin^{-1}\left(\dfrac{6}{11}\right)\) and \(\beta = 3\cos^{-1}\left(\dfrac{4}{9}\right)\), where inverse trigonometric functions take only the principal values.
Given below are two statements:
Statement I: \(\cos(\alpha+\beta) > 0\).
Statement II: \(\cos(\alpha) < 0\).
In the light of the above statements, choose the correct answer from the options given below:
- A Both Statement I and Statement II are true
- B Both Statement I and Statement II are false
- C Statement I is true but Statement II is false
- D Statement I is false but Statement II is true
Answer & Solution
Correct Answer
(A) Both Statement I and Statement II are true
Step-by-step Solution
Detailed explanation
We are given \(\alpha = 3\sin^{-1}\left(\dfrac{6}{11}\right)\) and \(\beta = 3\cos^{-1}\left(\dfrac{4}{9}\right)\). First, we find the range of \(\alpha\). Since \(\dfrac{1}{2} 0\). Thus, Statement I is true. Both Statement I and Statement II are true. Answer: Both Statement I…
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