Answer to Question #165811 in Trigonometry for Bright

Question

Prove that 1-cos2A/sin2A is tanA

Answer 1

$\frac{1-cos2A}{sin2A}=\frac{1-(1-2sin^2A)}{2sinA*cosA}$ ,

TRIGNOMETRIC DENTITY used : [Cos2A = 1-2sin²A]

[sin2A = 2sinA×cosA]

$\frac{1-cos2A}{sin2A}=\frac{1-1+2sin^2A}{2sinA\times cosA} = \frac{sinA}{cosA}=tanA$

So, $\frac{1-cos2A}{sin2A}=tanA$

LHS = RHS, Hence proved.