Quantitative Aptitude Ques 1612

Question: If $ \tan x=sin45{}^\circ \cdot cos45{}^\circ +\sin 30{}^\circ , $ then the value of x is

Options:

A) $ 30{}^\circ $

B) $ 45{}^\circ $

C) $ 60{}^\circ $

D) $ 90{}^\circ $

Show Answer

Answer:

Correct Answer: B

Solution:

  • [b] Given, $ \tan x=\sin 45{}^\circ \cdot \cos 45{}^\circ +\sin 30{}^\circ $
    $ \Rightarrow $ $ \tan x=\frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}+\frac{1}{2} $
    $ \Rightarrow $ $ \tan x=\frac{1}{2}+\frac{1}{2} $
    $ \Rightarrow $ $ \tan x=1=\tan 45{}^\circ $
    $ \Rightarrow $ $ x=45{}^\circ $
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