Question 1043458
a.  Cos^2 x=1/4
Cos x= +/- 1/2
This occurs at pi/3. 2pi/3, 4 pi/3, and 5*pi/3
===============
b.sin^2x-2sin x-3=0
(sin x -3)(sin x+1)=0
sin x cannot equal 3
sin x=-1
That occurs at 3pi/2.
===============
c.csc x-3 csc x sec x=0
csc x(1-3.sec x)=0
csc x cannot equal 0 because 1/sin x cannot equal 0.
Therefore, 1-3 sec x=0
3 sec x=1
sec x=1/3=1/cos x
cos x cannot equal 3.  No solution
===============
d.  sin (2x)=cos (2x)
sin x=cos x at pi/4,  5 pi/4, 9 pi/4 and 13 pi/4
Therefore, the two are equal at pi/8, 5 pi/8,, 9pi/8 and 13 pi/8