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CosA/(1+sinA)+(1+sinA)/cosA=2secA,prove it..​

Answer»

\mathfrak{\huge{Answer:-}} \\ \bold{ \frac{cosA}{1 + sinA} + \frac{1 + sinA}{cosA} = 2secA }\\ \frac{ {(cosA)}^{2} + {(1 + sinA)}^{2} }{( 1+ sinA)(cosA)} = 2secA \\ \frac{ {cos}^{2} A + 1 + {sin}^{2}A + 2sinA }{( 1+ sinA)(cosA)} = 2secA \\ \frac{ {cos}^{2} A + {sin}^{2} A + 1 + 2sinA}{(1 +sin A)(cosA)} = 2secA \\ \frac{1 + 1 + 2sinA}{(1 + sinA)(cosA)} =2secA \\ \frac{2 + 2sinA}{(1 + sinA)(cosA)} = 2secA \\ \frac{2(1 + sinA)}{(1 +sinA )(cosA)} = 2secA \\ \frac{2}{cosA} = 2secA \\ 2 \times \frac{1}{cosA} = 2secA \\ 2secA = 2secA \\ LHS=RHS \\Hence \: proved


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