Math, asked by Debjt, 1 year ago

Prove √1-cos a/√1+cos a=sin a/1+cos a​

Answers

Answered by spiderman2019
20

Answer:

Step-by-step explanation:

multiply numerator and denominator by √1+cosa

(√1-cosa)(√1+cosa) / (√1+cosa)²

= √1-cos²a / 1+cosa

= √sin²a/1+cosa = sina/1+cosa

= R.H.S

Answered by JeanaShupp
32

To prove:    \dfrac{\sqrt{1-\cos a} }{\sqrt{1+\cos a} } =\dfrac{\sin a}{1+\cos a}

Step-by-step explanation:

Consider L.H.S.

\dfrac{\sqrt{1-\cos a} }{\sqrt{1+\cos a} }

Now multiplying the numerator and denominator by \sqrt{1+\cos a} we get

\dfrac{\sqrt{1-\cos a} }{\sqrt{1+\cos a} }\times \dfrac{\sqrt{1+\cos a}}{\sqrt{1+\cos a}} \\\\= \dfrac{\sqrt{(1-\cos a)(1+\cos a)} }{(\sqrt{1+\cos a})^2 } \\\\=\dfrac{\sqrt{1-\cos^2 a} }{1+\cos a} \\\\ \therefore \text{as we know } \sin^2 a +\cos^2 a =1\\\\ = \dfrac{\sqrt{\sin^2 a} }{1+\cos a} = \dfrac{\sin a}{1+\cos a}

which is equal to R.H.S.

Hence, proved the required result

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