Trigonometric Identities Question 204
Question: If $ {{\tan }^{2}}\theta =2{{\tan }^{2}}\phi +1 $ ,then $ \cos 2\theta +{{\sin }^{2}}\phi $ equals
Options:
A) -1
B) 0
C) 1
D) none of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ {{\tan }^{2}}\theta =2{{\tan }^{2}}\phi +1 $ Or $ 1+{{\tan }^{2}}\theta =2(1+tan^{2}\phi ) $
$ \Rightarrow ,{{\sec }^{2}}\theta =2{{\sec }^{2}}\phi $
$ \Rightarrow ,{{\cos }^{2}}\phi =2{{\cos }^{2}}\theta $ $ =1+\cos 2\theta $
$ \Rightarrow \cos 2\theta ={{\cos }^{2}}\phi -1 $ $ =-{{\sin }^{2}}\phi $
$ \Rightarrow {{\sin }^{2}}\phi +\cos 2\theta =0 $
BETA
