If and , where the inverse trigonometric functions take principal values, then the…

MATHEMATICS · Multi correct · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

If α=3sin⁡−1(611)\alpha=3\sin^{-1}\left(\frac{6}{11}\right) and β=3cos⁡−1(49)\beta=3\cos^{-1}\left(\frac{4}{9}\right), where the inverse trigonometric functions take principal values, then the correct option(s) is/are (1) cos⁡β>0\cos\beta>0 (2) sin⁡β<0\sin\beta<0 (3) cos⁡(α+β)>0\cos(\alpha+\beta)>0 (4) cos⁡α<0\cos\alpha<0

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