Use trig identity:
sin 2x = 2sin x.cos x.
Substitute this value into the equation:
cos x - sin x (2sin x.cos x) = 0.
Put cos x into common factor:
cos x(1 - 2sin^2 x) = 0cosx(1−2sin2x)=0
Solve it by using trig table and unit circle:
a. cos x = 0 --> x = 0 and x = 2pix=2π
b. (1 - 2sin^2 x) = 0(1−2sin2x)=0
sin^2 x = 1/2sin2x=12
sin x = +- 1/sqrt2 = +- sqrt2/2sinx=±1√2=±√22
c. sin x = sqrt2/2sinx=√22 --> x = pi/4 and x = (3pi)/4x=π4andx=3π4
d. sin x = -sqrt2/2sinx=−√22 --> x = - pi/4 and x = -(3pi)/4x=−π4andx=−3π4
Arc (-pi/4)(−π4) is co-terminal to arc (7pi)/47π4
Arc ((-3pi)/4)(−3π4) is co-terminal to arc ((5pi)/4)(5π4)
Answers for (0, 2pi)(0,2π)
0, pi/3, (3pi)/4, (5pi)/4, (7pi)/4, 2pi0,π3,3π4,5π4,7π4,2π
