17. cos A-sin A cos A + sin A = sec...
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17. cos A-sin A cos A + sin A = sec 2A - tan 2A

JEE/Engineering Exams
Maths
Solution
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To peout: ( frac{cos A-sin A}{cos A+sin A}=sec 2 A-tan 2 A ) Taking ( R H S ) ( operatorname{Sel} 2 A-tan 2 A ) ( =frac{1}{cos A}-frac{sin 2 A}{cos A}=frac{(1-2 sin A cos A)}{cos ^{2} A-sin ^{2} A} ) ( =frac{(1-sin 2 A)}{cos 2 A}=frac{cos ^{2} A+sin ^{2} A-2 sin A cos A}{(cos A-sin A)(cos A+sin A)} ) ( =frac{(cos A-sin A)^{2}}{(cos A sin A)(cos A+sin A)} ) ( =cos A+sin A )
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