Quantitative Aptitude Ques 322

Question: The value of $ (\cos 0{}^\circ +\sin 45{}^\circ +\sin 30{}^\circ ) $ $ (sin90{}^\circ -cos45{}^\circ +\cos 60{}^\circ ) $ is

Options:

A) $ \frac{3}{2} $

B) $ \frac{7}{4} $

C) $ \frac{5}{4} $

D) $ \frac{3}{4} $

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ (\cos 0{}^\circ -\sin 45{}^\circ +\sin 30{}^\circ ) $ $ (\sin 90{}^\circ -\cos 45{}^\circ +\cos 60{}^\circ ) $ $ =( 1+\frac{1}{\sqrt{2}}+\frac{1}{2} )( 1-\frac{1}{\sqrt{2}}+\frac{1}{2} ) $ $ =( \frac{3}{2}+\frac{1}{\sqrt{2}} )( \frac{3}{2}-\frac{1}{\sqrt{2}} ) $ $ ={{( \frac{3}{2} )}^{2}}-{{( \frac{1}{\sqrt{2}} )}^{2}}=\frac{9}{4}-\frac{1}{2}=\frac{9-2}{4}=\frac{7}{4} $
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