मात्रात्मक योग्यता प्रश्न 2053
प्रश्न: $ \frac{(\sin \theta +\cos \theta )(\tan \theta +\cot \theta )}{\sec \theta +cosec\theta } $ किसके बराबर है?
विकल्प:
A) $ 1 $
B) $ 2 $
C) $ \sin \theta $
D) $ \cos \theta $
Show Answer
उत्तर:
सही उत्तर: A
समाधान:
- $ \frac{(\sin \theta +\cos \theta )(\tan \theta +\cot \theta )}{\sec \theta +cosec\theta } $ $ =\frac{(\sin \theta +\cos \theta )( \frac{\sin \theta }{\cos \theta }+\frac{\cos \theta }{\sin \theta } )}{\frac{1}{\cos \theta }+\frac{1}{\sin \theta }} $ $ =\frac{(\sin \theta +\cos \theta )( \frac{{{\sin }^{2}}\theta +{{\cos }^{2}}\theta }{\sin \theta \cos \theta } )}{\frac{\sin \theta +\cos \theta }{\sin \theta cos\theta }} $ $ =\frac{(\sin \theta +\cos \theta )( \frac{1}{\sin \theta \cos \theta } )}{\frac{\sin \theta +\cos \theta }{\sin \theta cos\theta }}=\frac{\frac{\sin \theta +\cos \theta }{\sin \theta \cos \theta }}{\frac{\sin \theta +\cos \theta }{\sin \theta \cos \theta }}=1 $ $ [\because {{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1] $
BETA
