Integral Calculus Question 273
Question: $ \int_{{}}^{{}}{\frac{cosec\theta -\cot \theta }{cosec\theta +\cot \theta }}\ d\theta = $
Options:
A) $ 2cosec\theta -2\cot \theta -\theta +c $
B) $ 2,cosec\theta -2\cot \theta +\theta +c $
C) $ 2,cosec\theta +2\cot \theta -\theta +c $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \int_{{}}^{{}}{\frac{cosec\theta -\cot \theta }{cosec\theta +\cot \theta },d\theta }=\int_{{}}^{{}}{{{(cosec\theta -\cot \theta )}^{2}}d\theta } $ $ =\int_{{}}^{{}}{cose{c^{2}}\theta ,d\theta }+\int_{{}}^{{}}{{{\cot }^{2}}\theta ,d\theta }-2\int_{{}}^{{}}{cosec\theta \cot \theta ,d\theta } $ $ =\int_{{}}^{{}}{(2cose{c^{2}}\theta -1),d\theta }-2\int_{{}}^{{}}{cosec\theta \cot \theta ,d\theta } $ $ =2cosec\theta -2\cot \theta -\theta +c. $
BETA
