How to PROVE: [(1-sin2x)/(sinx-cosx)] =sinx - cosx ?

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Answer 1 · 2018-04-24T17:37:05

Please see below.

We know that,

#color(red)((1)sin^2theta+cos^2 theta=1#

#color(blue)((2)sin2theta=2sinthetacostheta#

Here,

#[(1-sin2x)/(sinx-cosx)] =sinx - cosx#

We take,

#LHS=(color(red)(1)-sin2x)/(sinx-cosx) ...tocolor(red)(Apply(1)#

#=(color(red)(sin^2x+cos^2x)-color(blue)(sin2x))/(sinx-cosx)#

#=(sin^2x+cos^2x-color(blue)(2sinxcosx))/(sinx-cosx)...tocolor(blue)(Apply(2)#

#=(sinx-cosx)^2/(sinx-cosx)#

#=sinx-cosx#

#=RHS#