A) \[cot\theta -cosec\theta \]
B) \[sec\theta -\tan \theta \]
C) \[cosec\theta +cot\theta \]
D) \[tan\theta -sec\theta \]
Correct Answer: C
Solution :
(c) \[\sqrt{\frac{\sec \theta +1}{\sec \theta -1}}=\sqrt{\frac{\frac{1}{\cos \theta }+1}{\frac{1}{\cos \theta }-1}}\] \[=\sqrt{\frac{\frac{1+\cos \theta }{\cos \theta }}{\frac{1-\cos \theta }{\cos \theta }}}\] \[=\sqrt{\frac{1+\cos \theta }{1-\cos \theta }}=\sqrt{\frac{\left( 1+\cos \theta \right)\left( 1+\cos \theta \right)}{\left( 1-\cos \theta \right)\left( 1-\cos \theta \right)}}\] (Rationalizing the numerator and the denominator) \[=\sqrt{\frac{{{\left( 1+\cos \theta \right)}^{2}}}{1-{{\cos }^{2}}\theta }}=\frac{1}{\sin \theta }+\frac{\cos \theta }{\sin \theta }\] \[=cosec\theta +cot\theta .\]
You need to login to perform this action.
You will be redirected in
3 sec
