If theĀ identity 1-2sin^2a=2cos^2a+m is true, what is m?
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We are given that 1 - 2(sin a)^2 = 2* (cos a)^2 + m. We have to find m.
1 - 2(sin a)^2 = 2* (cos a)^2 + m
=> 1 - 2(sin a)^2 - 2* (cos a)^2 = m
=> 1 - 2[(sin a)^2 + (cos a)^2] = m
now use (sin a)^2 + (cos a)^2 = 1
=> 1 - 2*1 = m
=> 1 - 2 = m
=> m = -1
Therefore m = -1
We'll write (cos a)^2 with respect to (sin a)^2.
(cos a)^2 = 1 - (sin a)^2
We'll substitute (cos a)^2 by the equivalent expression:
1 - 2(sin a)^2 = 2[1 - (sin a)^2] + m
We'll remove the brackets:
1 - 2(sin a)^2 = 2 - 2(sin a)^2 + m
We'll eliminate 2(sin a)^2 both sides:
1 = 2 + m
We'll apply symmetric property:
m = 1 - 2
So m = -1
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