Question

√1-cos²A / 1+cos²A = SinA/ 1+cosA​

Answer 1

Answer:

=

1+cosa

sina

Step-by-step explanation:

Consider L.H.S.

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

1+cosa

1−cosa

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

1+cosa

we get

\begin{gathered}\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}\end{gathered}

1+cosa

1−cosa

×

1+cosa

1+cosa

=

(

1+cosa

)

2

(1−cosa)(1+cosa)

=

1+cosa

1−cos

2

a

∴as we know sin

2

a+cos

2

a=1

=

1+cosa

sin

2

a

=

1+cosa

sina

which is equal to R.H.S.

Hence, proved the required result