Replace in the equation #cos^2 x# by #( 1 - sin^2 x)# and put the equation in standard form:
#f(x) = 2 - 1 + sin^2 x - 4sin^2 (x/2) = 0#
Replace #sin^2 x# by #(4sin^2 (x/2).cos^2 (x/2))#
#f(x) = 1 + 4sin^2 (x/2).cos^2 (x/2) - 4sin^2 (x/2) = 0#
#f(x) = 1 + 4sin^2 (x/2)(cos^2 (x/2) - 1) = 0#
Since #(cos^2 (x/2) - 1) = - sin^2 (x/2)#, therefor:
#f(x) = 1 - 4sin^4 (x/2) = 0#
#4sin^4 (x/2) = 1#
#sin^4 (x/2) = 1/4# -->
#sin^2 (x/2) = 1/2# --> #sin x = +- 1/sqrt2 = +- sqrt2/2#
Trig table and unit circle -->
a. #sin x = sqrt2/2#. There are 2 solution arcs:
#x = pi/4# and #x = (3pi)/4#
b. #sin x = -sqrt2/2#. Two solution arcs:
#x = (5pi)/4# and #x = (7pi)/4#
