SATHEE: Quantitative Aptitude Ques 990

Quantitative Aptitude Ques 990

Question: If $ \sin \alpha \sec (30{}^\circ +\alpha )=1, $ $ (0<\alpha <60{}^\circ ), $ then the value of $ \sin \alpha +\cos 2\alpha , $ is

Options:

A) $ 1 $

B) $ \frac{2+\sqrt{3}}{2\sqrt{3}} $

C) $ 0 $

D) $ 2 $

Show Answer

Answer:

Correct Answer: A

Solution:

$ \sin \alpha \cdot sec(30{}^\circ +\alpha )=1 $

$ \Rightarrow $ $ \frac{\sin \alpha }{\cos (30{}^\circ +\alpha )}=1 $

$ \Rightarrow $ $ \frac{\sin \alpha }{\sin [90{}^\circ -(30{}^\circ +\alpha )]}=1 $

$ \Rightarrow $ $ \sin \alpha =\sin (60{}^\circ -\alpha ) $

$ \Rightarrow $ $ \alpha =60{}^\circ -\alpha $

$ \Rightarrow $ $ 2\alpha =60{}^\circ $
$ \Rightarrow $ $ \alpha =30{}^\circ $ Hence, $ \sin \alpha +\cos 2\alpha =\sin 30{}^\circ +\cos 60{}^\circ $ $ =\frac{1}{2}+\frac{1}{2}=1 $

Quantitative Aptitude Ques 989

Quantitative Aptitude Ques 991

Quantitative Aptitude Ques 990

Question: If $ \sin \alpha \sec (30{}^\circ +\alpha )=1, $ $ (0<\alpha <60{}^\circ ), $ then the value of $ \sin \alpha +\cos 2\alpha , $ is

Options:

Answer:

Solution:

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