Question

sinA (1+tanA)+cosA(1+cotA) =secA+cosecA​

Answer 1

Explanation:

$sinA(1+tanA)+cosA(1+cotA)=secA+cosecA \\ taking \: L.H.S \\=sinA(1+tanA)+cosA(1+cotA) \\= sinA(1+ \frac{sinA}{cosA} )+cosA(1+ \frac{cosA}{sinA} ) \\ = {sin}^{2}A (\frac{1}{sinA} + \frac{1}{cosA} )+ {cos}^{2} A( \frac{1}{cosA} + \frac{1}{sinA} ) \\ =( \frac{1}{cosA} + \frac{1}{sinA} )( {sin}^{2} A+ {cos}^{2} A) \\ =\frac{1}{cosA} + \frac{1}{sinA} \\ =secA+cosecA=R.H.S$

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