Question

Simplify this √(1+sinA) /(1-si.nA)​

Answer 1

Given :-

• $\sf{\sqrt{\dfrac{1+sinA}{1-sinA} } }$

To Simplify :-

• $\sf{\sqrt{\dfrac{1+sinA}{1-sinA} } }$

Identities need to be used :-

• sin²A + cos²A = 1

• sec A = 1/cos A

• tan A = sin A/cos A

Solution :-

Given that,

$\sf{\sqrt{\dfrac{1+sinA}{1-sinA} } }\\\\\\\sf{=\sqrt{\dfrac{(1+sinA)(1+sinA)}{(1-sinA)(1+sinA)} } }\\\\\\\sf{=\sqrt{\dfrac{(1+sinA)^2}{(1)^2-(sinA)^2} } }\\\\\\\sf{=\sqrt{\dfrac{(1+sinA)^2}{1-sin^2A} } }\\\\\\\sf{=\sqrt{\dfrac{(1+sinA)^2}{cos^2A} } }\\\\\\\sf{=\sqrt{\dfrac{(1+sinA)^2}{(cosA)^2} } }\\\\\\\sf{=\sqrt{\bigg(\dfrac{1+sinA}{cosA} \bigg)^2 } }\\\\\\\sf{=\dfrac{1+sinA}{cosA} } \\\\\\\sf{=\dfrac{1}{cosA}+\dfrac{sinA}{cosA} }\\\\\\\sf{=secA+tanA}$

Hence,

sec A + tan A is the required answer.