PRECALC
solve the equation
1. cos(θ) − sin(θ) = 1
2.2 cos(θ) tan(θ) + tan(θ) = 1 + 2 cos(θ)
3. sin(θ) cos(3θ) + cos(θ) sin(3θ) = 0
4. sin(2θ) cos(θ) − cos(2θ) sin(θ) = 1/2
5. cos(2θ) + cos(θ) = 2
6. cos(2θ) + sin2(θ) = 0

#1, look how I did this similar problem, and follow the same steps
http://www.jiskha.com/display.cgi?id=1461697741
#2
2 cos(θ) tan(θ) + tan(θ) = 1 + 2 cos(θ)
2cosθtanθ  2cos + tanθ  1 = 0
2cosθ(tanθ  1) + (tanθ 1) = 0
by grouping:
(tan  1)(2cosθ + 1) = 0
tanθ = 1 or cosθ = 1/2
θ = 45 or θ = 225 or θ = 240 or θ =300 degrees
in radians: θ = π/4, 5π/4, 4π/3, 5π/3
#3 and #4 are based on the formula
sin(A ± B) = sinAcosB ± cosAsinB
I will do #4, you do #3
sin(2θ) cos(θ) − cos(2θ) sin(θ) = 1/2
sin(2θ  θ) = 1/2
sin θ = 1/2
θ = 30 degrees or θ = 150 degrees
or θ = pi/6 or 5pi/6
#5
I will assume you mean:
cos(2θ) + sin^2 (θ) = 0
cos^2 θ  sin^2 θ + sin^2 θ = 0
cos^2 θ = 0
cosθ = 0
θ = 90 or θ = 270 degrees
θ = pi/2 or 3pi/2posted by Reiny
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