$sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A .$

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sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A .

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Text solutionVerified

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

= sin A (1 + \frac{sin A}{cos A}) + cos A (1 + \frac{cos A}{sin A})

= sin A + \frac{sin ^{2} A}{cos A} + cos A + \frac{cos ^{2} A}{sin A}

= \frac{sin ^{2} A + cos ^{2} A}{sin A} + \frac{sin ^{2} A + cos ^{2} A}{cos A}

= sec A + cosec A

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Question Text	$sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A .$
Answer Type	Text solution:1
Upvotes	150