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Inverse Trigonometric Functions question

2015 · Shift 2 · Q32

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PYQ Library
JEE Advanced
Mathematics
Inverse Trigonometric Functions
2015 · Shift 2 · Q32

Inverse Trigonometric Functions question

2015 · Shift 2 · Q32

JEE AdvancedMathematicsInverse Trigonometric FunctionsMultiple correct+4 / −1

If

\alpha

= 3{\sin ^{ - 1}}\left( {{6 \over {11}}} \right)

and

\beta = 3{\cos ^{ - 1}}\left( {{4 \over 9}} \right),

where the inverse trigonimetric functions take only the principal values, then the correct options(s) is (are)

A
$cos\beta \gt 0$
B
$\sin \beta \lt 0$
C
$\cos \left( {\alpha + \beta } \right) \gt 0$
D
$\cos \alpha \lt 0$

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