A) \[2\sec \theta \]
B) \[\sec \theta \]
C) \[2co\sec \theta \]
D) None of these
Correct Answer: C
Solution :
(c): \[\sqrt{\frac{(1+cos\,\theta )(1+cos\,\theta )}{(1-cos\,\theta )(1+cos\,\theta )}}+\sqrt{\frac{(1-cos\,\theta )(1-cos\,\theta )}{(1+\cos \,\theta )(1-cos\theta )}}\] \[=\sqrt{\frac{{{(1+cos\,\theta )}^{2}}}{1-{{\cos }^{2}}\theta }}+\sqrt{\frac{{{(1-cos\theta )}^{2}}}{1-{{\cos }^{2}}\theta }}\] \[=\frac{1+\cos \theta }{\sin \theta }+\frac{1-\cos \theta }{\sin \theta }=\frac{1+\cos \theta +1-\cos \theta }{\sin \theta }\] \[=\frac{2}{\sin \theta }=2\,\,\cos ec\theta \]
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