Answer:
\[L.H.S.=(sec\text{ }A-cos\text{ }A)\text{ (}cot\text{ }A+tan\text{ }A)\] \[=\left( \frac{1}{\cos \,A}-\cos A \right)\left( \frac{\cos A}{\sin A}+\frac{\sin A}{\cos A} \right)\] \[=\left( \frac{1-{{\cos }^{2}}A}{\cos A} \right)\left( \frac{{{\cos }^{2}}A+{{\sin }^{2}}A}{\sin A\cos A} \right)\] \[=\frac{{{\sin }^{2}}A}{\cos A}\times \frac{1}{\sin A\cos A}\] \[[\because \,\,co{{s}^{2}}A+si{{n}^{2}}A=1]\] \[=\frac{\sin A}{\cos A}\times \frac{1}{\cos A}\] \[=\tan A.\sec A=R.H.S.\] Hence Proved.
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