A) \[\sin A\]
B) \[\cos A\]
C) \[\sec A\]
D) \[\text{cosec}\,\,A\]
Correct Answer: A
Solution :
\[\frac{(1-\sin A\cos A)({{\sin }^{2}}A-{{\cos }^{2}}A)}{\cos A\,\,(\sec A-\text{cosec}\,\,\text{A)(si}{{\text{n}}^{3}}A+{{\cos }^{3}}A)}\] |
\[=\frac{(1-\sin A\cos A)({{\sin }^{2}}A-{{\cos }^{2}}A)}{\left[ \begin{align} & \cos A\left( \frac{1}{\cos A}-\frac{1}{\sin A} \right)(\sin A+\cos A) \\ & ({{\sin }^{2}}A+{{\cos }^{2}}A-\sin A\cos A) \\ \end{align} \right]}\] |
\[=\frac{(1-\sin A\cos A)(\sin A\cdot \cos A)}{\cos A\,\,(\sin A-\cos A)(\sin A+\cos A)}\] |
\[\frac{(\sin A+\operatorname{cosA})(sinA-cosA)}{1-\sin A\cos A}\] |
\[=\sin A\] |
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