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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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 =...

See
This Answer Now

Start your subscription to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your Subscription

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

Approved by eNotes Editorial Team