Question

prove that 1+cosA+sinA/1+cosA-sinA=sac+tan​

Answer 1

         

$\Rightarrow\ \boxed{ LHS } \\ \\ \\ \Rightarrow\ \boxed{\frac{1+\cos A+\sin A}{1+\cos A-\sin A}} \\ \\ \\ \Rightarrow\ \boxed{\frac{(1+\cos A+\sin A)\sec A}{(1+\cos A-\sin A)\sec A}} \\ \\ \\ \Rightarrow\ \boxed{\frac{\sec A+\cos A \cdot \sec A+\sin A \cdot \sec A}{\sec A+\cos A \cdot \sec A-\sin A \cdot \sec A}} \\ \\ \\ \Rightarrow\ \boxed{\frac{\sec A+1+\tan A}{\sec A+1-\tan A}} \\ \\ \\ \Rightarrow\ \boxed{\frac{\sec A+\tan A+1}{\sec A-\tan A+1}}$

$\Rightarrow\ \boxed{\frac{(\sec A+\tan A+1)(\sec A+\tan A)}{(\sec A-\tan A+1)(\sec A+\tan A)}} \\ \\ \\ \Rightarrow\ \boxed{\frac{(\sec A+\tan A+1)(\sec A+\tan A)}{\sec^2A-\tan^2A+\sec A+\tan A}} \\ \\ \\ \Rightarrow\ \boxed{\frac{(\sec A+\tan A+1)(\sec A+\tan A)}{1+\sec A+\tan A}} \\ \\ \\ \Rightarrow\ \boxed{\frac{(\sec A+\tan A+1)(\sec A+\tan A)}{\sec A+\tan A+1}} \\ \\ \\ \Rightarrow\ \boxed{\sec A+\tan A} \\ \\ \\ \Rightarrow\ \boxed{ RHS }$

$Hence proved!!! \\ \\ \\ Thank you. :-))$

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