If the identity 1-2sin^2a=2cos^2a+m is true, what is m?

justaguide | College Teacher | (Level 2) Distinguished Educator

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

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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