SSC Sample Paper Mock Test-20 SSC CGL Tear-II Paper-1

What is the simplest value of \[\frac{(1-\sin A\cos A)({{\sin }^{2}}A-{{\cos }^{2}}A)}{\cos A\,\,(\sec A-\text{cosec}\,\,A)(si{{n}^{3}}A+{{\cos }^{3}}A)}?\]

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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SSC Sample Paper Mock Test-20 SSC CGL Tear-II Paper-1

question_answer What is the simplest value of \[\frac{(1-\sin A\cos A)({{\sin }^{2}}A-{{\cos }^{2}}A)}{\cos A\,\,(\sec A-\text{cosec}\,\,A)(si{{n}^{3}}A+{{\cos }^{3}}A)}?\] A) \[\sin A\] B) \[\cos A\] C) \[\sec A\] D) \[\text{cosec}\,\,A\]

What is the simplest value of \[\frac{(1-\sin A\cos A)({{\sin }^{2}}A-{{\cos }^{2}}A)}{\cos A\,\,(\sec A-\text{cosec}\,\,A)(si{{n}^{3}}A+{{\cos }^{3}}A)}?\]

A) \[\sin A\]

B) \[\cos A\]

C) \[\sec A\]

D) \[\text{cosec}\,\,A\]