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**