Integral Calculus Question 215
Question: $ \int_{{}}^{{}}{\frac{\cos x-1}{\cos x+1}\ dx=} $
[MP PET 1989, 92]
Options:
A) $ 2\tan \frac{x}{2}-x+c $
B) $ \frac{1}{2}\tan \frac{x}{2}-x+c $
C) $ x-\frac{1}{2}\tan \frac{x}{2}+c $
D) $ x-2\tan \frac{x}{2}+c $
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Answer:
Correct Answer: D
Solution:
$ \int_{{}}^{{}}{\frac{\cos x-1}{\cos x+1},dx=-\int_{{}}^{{}}{{{\tan }^{2}}\frac{x}{2},dx}} $ $ =-\int{( {{\sec }^{2}}\frac{x}{2}-1 ),dx}=\int{( 1-{{\sec }^{2}}\frac{x}{2} )dx=x-2\tan \frac{x}{2}+c} $ .
BETA
