Question #483b0

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Answer 1 · 2016-11-06T07:41:46

$x = π + 2 k π or x = \frac{π}{4} + k π$ $x=pi+2kpi or x=pi/4+kpi$

Since ${cos}^{2} (\frac{x}{2}) = \frac{1 + cos x}{2} and tan x = \frac{sin x}{cos x}$ $cos^2(x/2)=(1+cosx)/2 and tanx=sinx/cosx$ ,

by substituting you have:

$cancel2(1+cosx)/cancel2=sinx/cosx+sinx$

$cosx+cos^2x=sinx+sinxcosx and cosx!=0$

$cosx+cos^2x-sinx-sinxcosx=0 and cosx!=0$

$cosx(1+cosx)-sinx(1+cosx)=0 and cosx!=0$

$(1+cosx)(cosx-sinx)=0$

$1+cosx=0 or cosx-sinx=0$

$cosx=-1 or cosx=sinx$

$x=pi+2kpi or x=pi/4+kpi$