Question

prove that sin2A/1-cos2A=cotA

Answer 1

Hey there!

L.H.S

=sin2A/1-cos2A

= 2sinAcosA/1-(1-2sin²A)

= 2sinAcosA/2sin²A

=cosA/sinA

=cotA

=R.H.S

hope helped !!

Answer 2

Solution:

Given

LHS =$\frac{sin2A}{1-cos2A}$

= $\frac{sin2A}{(cos^{2}A+cos^{2})-(cos^{2}A-sin^{2}A)}$

/* Since ,

i) 1 = cos²A + sin²A

ii ) cos2A = cos²A-sin²A */

= $\frac{2sinAcosA}{sin^{2}A+cos^{2}A-cos^{2}A+sin^{2}A}$

/* we know that,

sin2A = 2sinAcosA */

= $\frac{2sinAcosA}{2sin^{2}A}$

After cancellation, we get

= $\frac{cosA}{sinA}$

= $cotA$

= $RHS$

Therefore,

$\frac{sin2A}{1-cos2A}$

=$cotA$

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