Prove the identity by transforming the left side of the equation to match the right side.Do not manipulate both sides.Work with the left side only!1+𝑡𝑎𝑛𝑥1−𝑡𝑎𝑛𝑥=𝑐𝑜𝑠(2𝑥)1−𝑠𝑖𝑛(2𝑥)

Answer 1

(1+tanx)/(1-tanx) = cos(2x)/(1-sin(2x))

(1+sinx/cosx)/(1-sinx/cosx)

(cosx+sinx)/(cosx-sinx)

(cosx+sinx)/(cosx-sinx) • (cosx-sinx)/(cosx-sinx)

(cos²(x) -sin²(x))/(cosx - sinx)² Double angle: cos²(x)-sin²(x) = cos(2x))

cos(2x)/(cos²(x)-2cos(x)sin(x)+sin²(x)) Note: cos²(x)+sin²(x) = 1

cos(2x)/(1-2cos(x)sin(x)) Double angle: 2cos(x)sin(x) = sin(2x)

cos(2x)/(1-sin(2x)) = cos(2x)/(1-sin(2x))