Find all the solutions to the equation in the interval 0,2pi? Sin(x+pi/2)-cos^2x=0

1 Answer
Feb 13, 2018

#x= 0, pi/2 and (3pi)/2#

Explanation:

Use #sin(A + B) = sinAcosB +sinBcosA#.

#sinxcos(pi/2) + sin(pi/2)cosx - cos^2x = 0#

#sinx(0) + cosx - cos^2x= 0 #

#-cosx(cosx - 1) = 0#

#cosx = 0 or cosx = 1#

#x= pi/2, (3pi)/2 or 0#

Hopefully this helps!