Expert: Paul Klarreich - 3/2/2009

Question
Find all solutions of 2-sin^2x=2cos^2(x/2)

Answer
Questioner:   Marshall
Category:  Advanced Math
Private:  No
 
Subject:  Trig
Question:  Find all solutions of 2-sin^2x=2cos^2(x/2)

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2 - sin^2(x) = 2 cos^2(x/2)

Use a 'power-reducing'/half-angle formula:

http://www.sosmath.com/trig/Trig5/trig5/trig5.html

with u = x/2:

                1 + cos x
2 - sin^2(x)= 2 (----------)
                    2

2 - sin^2(x) =  1 + cos x
             
2 - (1 - cos^2(x)) =  1 + cos x   << make it all cosines:

2 - (1 - c^2) =  1 + c  << abbreviate

2 - 1 + c^2 =  1 + c

1 + c^2 =  1 + c

c^2 = c

Cos x = 0 and cos x = 1.


You can take it from here.