What are all the values for A between 0 to 360 degrees? sinA+1=tanA+cosA

1 Answer
Apr 12, 2018

#A = 0, 45˚, 225˚#

Explanation:

We rewrite #tanA = sinA/cosA#.

#sinA + 1 = sinA/cosA + cosA#

#sinA + 1 = (sinA +cos^2A)/cosA#

#sinAcosA + cosA = sinA + cos^2A#

#0 = cos^2A + sinA - cosA - sinAcosA#

#0 = cosA(cosA - 1) - sinA(cosA - 1)#

#0 = (cosA -sinA)(cosA - 1)#

#cosA = sinA or cosA = 1#

The first equation is clearly true when #A = 45˚# or #225˚#. For the second equation, this only occurs once at #A = 0˚#. The graph confirms:

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Hopefully this helps!