SOLUTION: Hello,Can you please help me solve this problem: 1.Solve the following equation for x e [0, 2pi): cos^2(x+pi/2)- sin^2 (x+pi/2) =1 Thank you very much. I appreciate your

Question 960613: Hello,Can you please help me solve this problem:
1.Solve the following equation for x e [0, 2pi):
cos^2(x+pi/2)- sin^2 (x+pi/2) =1
Thank you very much. I appreciate your help.
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!



Recognize that the left side is the right side of the identity
 with  substituted for q.

So the equation becomes:





Adding p to an angle moves it from
1. 1st quadrant to 3rd quadrant or
2. 2nd quadrant to 4th quadrant or
3. 3rd quadrant to 1st quadrant or
4. 4th quadrant to 2nd quadrant or
5. 0 to p

In any case the cosine of an angle has the opposite sign when 
p is added to it.  IOW,  is an identity.

Using it on the left side:





since , multiply that by 2, ,
so to find all solutions for x between 0 and 2p,
we must take all possible values of 2x between
0 and 4p. 





Edwin

RELATED QUESTIONS
solve the equation, [0, 2pi) a)... (answered by lwsshak3)

Can someone please help me with this problem? If csc(x)=6, for 90degrees < x <... (answered by KMST,Gogonati)

Solve the following equation: cos(x/3 - pi/4) = 1/2 , x is btw 0 and... (answered by Alan3354)

Please help me solve this problem Solve the equation on the interval 0 < x < 2(pi) (answered by jim_thompson5910)

Solve the following equation for x: cos x = -1, for the interval 0 < x < 2... (answered by richard1234)

Please help me solve this equation: {{{ cos^2(x)+2sin(x)cos(x)-sin^2(x)=0 }}} with the... (answered by Edwin McCravy)

Please solve the equation sin*(2*x+(pi/3)) = 1/2 for x is [0,pi] Show... (answered by josmiceli)

Solve 2 sin^2 x + cos x -2=0 on the interval -pi< x <... (answered by lwsshak3)

Solve the equation for 0≤x≤{{{2pi}}}. Write your answer as a multiple of... (answered by KMST)