Trigonometric Identities Question 149
Question: If $ \tan \theta +\sec \theta =e^{x}, $ then $ \cos \theta $ equals
[AMU 2002]
Options:
A) $ \frac{(e^{x}+{e^{-x}})}{2} $
B) $ \frac{2}{(e^{x}+{e^{-x}})} $
C) $ \frac{(e^{x}-{e^{-x}})}{2} $
D) $ \frac{(e^{x}-{e^{-x}})}{(e^{x}+{e^{-x}})} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \tan \theta +\sec \theta =e^{x} $ ?..(i)
$ \therefore ,\sec \theta -\tan \theta ={e^{-x}} $ ?..(ii) From (i) and (ii), $ ,2\sec \theta =e^{x}+{e^{-x}},\Rightarrow ,\cos \theta =\frac{2}{e^{x}+{e^{-x}}}. $
BETA
