Question 764992: solve the equation cos theta - tan theta * cos theta = 0 for 0< theta < 2 pi Found 2 solutions by stanbon, DrBeeee:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! solve the equation
cos theta - tan theta * cos theta = 0 for 0< theta < 2 pi
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cos - (sin/cos)*cos = 0
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cos-sin = 0
cos(theta) = sin(theta)
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theta = pi/4 or theta = (5/4)pi
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Cheers,
Stan H.
You can put this solution on YOUR website! Given:
(1) cosx - tanx*cosx = 0 or factoring becomes
(2) cosx*(1 - tanx) = 0
When the product of two factors is zero, the solution is that either or both factors can be equal to zero. In this case we can have
(3) cosx = 0 and/or
(4) 1 - tanx = 0
The solution to (3) is
(5) x = pi/2 and 3*pi/2
The solution to (4) is
(6) tanx = 1 or
(7) x = pi/4 and 3*pi/4
Answer: theta = (pi/4,pi/2,3*pi/4,3*pi/2) or (45,90,225,270) degrees
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