Question

prove the following identity cos A/1+sinA + 1+sin A/CosA= 2secA​

Answer 1

Answer:

$\frac{cosA}{1 + sinA} + \frac{1 + sinA}{cosA} = 2secA \\ \frac{ {(cosA)}^{2} + {(1 + sinA)}^{2}}{cosA(1 + sinA)} = 2secA \\ \frac{ {cos}^{2}A + 1 + 2sinA + {sin}^{2} A}{cosA(1 + sinA)} = 2secA \\ \frac{ {cos}^{2}A + {sin}^{2} A + 1 + 2sinA }{cosA(1 + sinA)} = 2secA \\ \frac{1 + 1 + 2sinA}{cosA(1 + sinA)} = 2secA \\ \frac{2 + 2sinA}{cos(1 + sinA)} = 2secA \\ \frac{2(1 + sinA)}{cos(1 + sinA)} = 2secA \\ \frac{2}{cosA} = 2secA \\ 2 \times \frac{1}{cosA} = 2secA \\ 2secA = 2secA \\ LHS=RHS \\ Hence \: proved$