Question

Question #b2d07

Answer 1

`frac{1-siny}{1+siny} =(secy - tan y)^2`

Left side - multiply by the conjugate of the denominator over itself:
`"LS "=frac{(1-siny)(1-siny)}{(1+siny)(1-siny)}`

`= frac{(1-siny)^2}{1-sin^2y}`

Simplify the denominator using the pythagorean trigonometric identity:
`= color(blue)(frac{(1-siny)^2}{cos^2y})`

Right side - write in terms of `sin` and `cos`

`"RS" = (1/cosy - siny/cosy)^2`

`= color(blue)(frac{(1-siny)^2}{cos^2y})`

`frac{(1-siny)^2}{cos^2y} = frac{(1-siny)^2}{cos^2y}`

`color(blue)( :."LS" = "RS")`