SATHEE: Quantitative Aptitude Ques 324

Quantitative Aptitude Ques 324

Question: The value of $ {{\sec }^{4}}A,(1-{{\sin }^{4}}A)-2{{\tan }^{2}}A $ is

Options:

A) $ \frac{1}{2} $

B) 1

C) 0

D) 2

Show Answer

Answer:

Correct Answer: B

Solution:

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

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Quantitative Aptitude Ques 324

Question: The value of $ {{\sec }^{4}}A,(1-{{\sin }^{4}}A)-2{{\tan }^{2}}A $ is

Options:

Answer:

Solution:

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