A) \[\cos A-\tan A\]
B) \[\cos A-\cot A\]
C) \[\sec A-\cot A\]
D) \[\sec A-\tan A\]
Correct Answer: D
Solution :
Given expression\[=\frac{\sqrt{1-\sin A}}{\sqrt{1+\sin A}}\times \frac{\sqrt{1-\sin A}}{\sqrt{1-\sin A}}\] \[\,=\frac{(1-\sin A)}{\sqrt{1-{{\sin }^{2}}A}}\] \[=\frac{(1-\sin A)}{\sqrt{{{\cos }^{2}}}A}=\frac{(1-\sin A)}{\cos A}\] \[=\left( \frac{1}{\cos A}-\frac{\sin A}{\cos A} \right)\] \[=\sec A-\tan A\]
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