How to solve the equation cos(2x+ pi/2)=cos(x- pi/2)?

Expert Answers

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If cos(A) = cos(B), then

case 1: A = n*2Pi+B, where n is an integer,

case2:  A = n*2Pi-B

A = 2x+pi/2,  B = x-pi/2

 

case 1:

2x+pi/2 = n*2pi+x-pi/2

x + pi = n*2pi

x = pi(2n-1), or x = -pi for n=0

 

case 2:

2x+pi/2 = n*2pi-(x-pi/2)

2x+pi/2 = n*2pi-x+pi/2

3x = n*2pi

x = 2nPi/3, or x = 0 for n=0

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