Inverse Trigonometric Functions Question 93
Question: What is the value of: $ \cos [ {{\tan }^{-1}}{ \tan ( \frac{15\pi }{4} ) } ]? $
Options:
A) $ -\frac{1}{\sqrt{2}} $
B) 0
C) $ \frac{1}{\sqrt{2}} $
D) $ \frac{1}{2\sqrt{2}} $
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Answer:
Correct Answer: C
The given trigonometric expression is: $ \cos [ {{\tan }^{-1}}{ \tan ( \frac{15\pi }{4} ) } ] $
$ =\cos [ {{\tan }^{-1}}{ \tan ( 4\pi -\frac{\pi }{4} ) } ] $
$ =\cos [ {{\tan }^{-1}}{ -\tan \frac{\pi }{4} } ]=\cos [ {{\tan }^{-1}}\tan ( \frac{-\pi }{4} ) ] $ Since, $ {{\tan }^{-1}}\theta $ is defined for $ \frac{-\pi }{2}<\theta <\frac{-\pi }{2} $
$ =\cos ( \frac{-\pi }{4} ) $
$ \cos \frac{\pi }{4}=\frac{1}{\sqrt{2}} $ [since $ \cos (-\theta )=cos\theta $ ]
BETA
