Quantitative Aptitude Ques 1352

Question: Value of $ {{\sec }^{2}}\theta +\frac{{{\sin }^{2}}\theta -2{{\sin }^{4}}\theta }{2{{\cos }^{4}}\theta -{{\cos }^{2}}\theta } $ is

Options:

A) $ 1 $

B) $ 2 $

C) $ -1 $

D) $ 0 $

Show Answer

Answer:

Correct Answer: A

Solution:

  • $ {{\sec }^{2}}\theta -\frac{{{\sin }^{2}}\theta -2{{\sin }^{4}}\theta }{2{{\cos }^{4}}\theta -{{\cos }^{2}}\theta } $ $ ={{\sec }^{2}}\theta =\frac{{{\sin }^{2}}\theta ,(1-2{{\sin }^{2}}\theta )}{{{\cos }^{2}}\theta ,(2{{\cos }^{2}}\theta -1)} $ $ ={{\sec }^{2}}\theta -\frac{{{\sin }^{2}}\theta \cdot \cos 2\theta }{{{\cos }^{2}}\theta \cdot \cos 2\theta } $ $ [\because \cos 2\theta =1-2{{\sin }^{2}}\theta =2{{\cos }^{2}}\theta -1] $ $ ={{\sec }^{2}}\theta -{{\tan }^{2}}\theta =1 $
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