Trigonometric Identities Question 221
Question: If $ \sin \theta =\frac{12}{13}( 0<\theta <\frac{\pi }{2} ) $ and $ \cos \phi =-\frac{3}{5},( \pi <\phi <\frac{3\pi }{2} ) $ Then $ \sin (\theta +\phi ) $ will be
Options:
A) $ \frac{-56}{61} $
B) $ \frac{-56}{65} $
C) $ \frac{1}{65} $
D) $ -56 $
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ \sin \theta =\frac{12}{13} $ $ \cos \theta =\sqrt{1-{{\sin }^{2}}\theta }=\sqrt{1-{{( \frac{12}{13} )}^{2}}}=\frac{5}{13} $ and $ \cos \phi =\frac{-3}{5},,\sin \phi =\sqrt{1-\frac{9}{25}}=\frac{-4}{5}, $ $ [ \because \pi <\phi <\frac{3\pi }{2} ] $ Now, $ \sin (\theta +\phi )=\sin \theta .\cos ,\phi +\cos \theta .\sin \phi $ $ =( \frac{12}{13} )( \frac{-3}{5} )+( \frac{5}{13} )( \frac{-4}{5} )=\frac{-36}{65}-\frac{20}{65}=\frac{-56}{65} $
BETA
