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Solve A(1+ A)+ A(1+ A).

Question

Solve $sin A (1 + tan A) + cos A (1 + cot A)$ .

sec A + cosec A

sin A + cos A

tan A + cot A

cos A + sin A

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sin A (1 + tan A) + cos A (1 + cot A)

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Text solutionVerified

s in A (1 + t an A) + cos A (1 + co t A)

\Rightarrow s in A (1 + \frac{sin A}{cos A}) + cos A (1 + \frac{cos A}{sin A})

\Rightarrow \frac{sin A}{cos A} (sin A + cos A) + \frac{cos A}{sin A} (sin A + cos A)

\Rightarrow (sin A + cos A) [\frac{sin ^{2} A + cos ^{2} A}{sin A \cdot cos A}]

\Rightarrow \frac{sin A}{sin A \cdot cos A} + \frac{cos A}{sin A \cdot cos A}

\Rightarrow sec A + cosec A

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