Trigonometric Identities Question 307
Question: If $ \tan \theta =t, $ then $ \tan 2\theta +\sec 2\theta = $
[MP PET 1999]
Options:
A) $ \frac{1+t}{1-t} $
B) $ \frac{1-t}{1+t} $
C) $ \frac{2t}{1-t} $
D) $ \frac{2t}{1+t} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \tan 2\theta =\frac{2\tan \theta }{1-{{\tan }^{2}}\theta },\cos 2\theta =\frac{1-{{\tan }^{2}}\theta }{1+{{\tan }^{2}}\theta } $ $ \tan 2\theta +\sec 2\theta =\frac{2t}{1-t^{2}}+\frac{1+t^{2}}{1-t^{2}}=\frac{{{(1+t)}^{2}}}{(1-t)(1+t)}=\frac{1+t}{1-t} $ .
BETA
