Question 674206: find all solutions of the equation sec(theta)tan(theta)-cos(theta)cot(theta)=sin(theta)
find the solutions in the interval [0,2pi]
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find all solutions of the equation sec(theta)tan(theta)-cos(theta)cot(theta)=sin(theta)
find the solutions in the interval [0,2pi]
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secxtanx-cosxcotx=sinx
1/cosx*sinx/cosx-cosx*cosx/sinx=sinx
sinx/cos^2x-cos^2x/sinx=sinx
multiply each term by sinx
sin^2x/cos^2x-cos^2x=sin^2x
sin^2x/cos^2x=sin^2x+cos^2x
sin^2x/cos^2x=1
tan^2x=1
tanx=±√1=±1
x=π/4, 3π/4, 5π/4, and 7π/4
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