Question

Prove that ( frac{cos A}{1-tan A}+frac{sin ^{2} A}{sin A-cos A}=sin A+cos A )

NEET/Medical Exams

Physics

Solution

470

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Prove that cosA/1−tanA+sin2A/sinA−cosA=sinA+cosA

( begin{aligned} frac{cos A}{1-tan A}+frac{sin ^{2} A}{sin A-cos A} &=frac{cos A}{1-sin A}+frac{sin ^{2} A}{sin A-cos A} =& frac{cos ^{2} A}{cos A-sin A}-frac{sin ^{2} A}{cos A-sin A} =& frac{cos ^{2} A-sin ^{2} A}{cos A-sin A} =&(cos A-sin A)(cos A+sin A) & cos A-sin A =& cos A+sin A =& R H S text { Heres proved. } end{aligned} )