Solve the equation frac{1-sin x}{1+sin x}=(sec x-tan x)^{2}

Nannie Mack 2020-10-28 Answered
Solve the equation 1sinx1+sinx=(secxtanx)2
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Expert Answer

hosentak
Answered 2020-10-29 Author has 100 answers
(sec(x)tan(x))2=(1cos(x)sin(x)cos(x))2
=(1sin(x)cos(x))2
=(1sin(x))2cos2(x)
=(1sin(x))21sin2(x)
=(1sin(x))2(sin(x)+1)(sin(x)1)
=1sin(x)sin(x)+1
=1sin(x)1+sin(x)
Therefore
1sin(x)1+sin(x)=(sec(x)tan(x))2
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