Question

all T1 Selo SECU Prove that sin A (1+tan A) + cos A (1 + cot A) = sec A + cosec A. 08

11th - 12th Class

Maths

Solution

118

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[ begin{array}{l} sin A(1+tan A)+cos A(1+cot A) =sec A+operatorname{cosec} A text { Taking } L cdot mid-1 cdot int_{cos A}+frac{sin ^{2} A}{cos A}+cos A+frac{cos ^{2} A}{sin A} sin A+frac{sin A}{=} frac{sin ^{2} A+cos ^{2} A}{cos A}=frac{sin ^{2} A+cos ^{2} A}{sin A} =frac{1}{sin A} =frac{1}{cos A} end{array} ]