Question 733015: Sinx+tanx/1+secx=2cos^2x
Im having trouble solving this one. Help would be greatly appreciated. Thanks.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Sinx+tanx/1+secx=2cos^2x
Im having trouble solving this one. Help would be greatly appreciated. Thanks.
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Sinx+tanx/1+secx=2cos^2x
[(sinx+(sinx/cosx)]/[(1+(1/cosx)]=2(1-sin^2x)
((cosxsinx+sinx)/cos)/((cosx+1)/cosx)=2-2sin^2x
((sinx(1+cosx)/(cosx+1)=2-2sin^2x
sinx=2-2sin^2x
2sin^2x+sinx-2=0
solve for sinx using quadratic formula:
a=2, b=1,c=-2
sinx=[-1±√(1-4*2*-2)]/2*2=-1±√17/4
sinx=(-1+√17)/4≈0.781
x≈51.35º
or
sinx≈-1.281(reject, (-1 < sinx < 1)
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