Question #b2d07

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Answer 1 · 2017-10-18T02:09:11

#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")#