Write 5- cos2t +12sin 2t in form of Acos(2t −θ ).?

12 sin 2t - 5 cos 2t = a [ cos 2t - Ө ]

12 sin 2t - 5 cos 2t = acos 2t sin Ө + asin 2t cos Ө

12 = a cos Ө
- 5 = a sin Ө

169 = a²
a = 13

tan Ө = - 5/12 and Ө in 4th quadrant
Ө = 337.4⁰

a [ cos 2t - Ө ] = 13 [ cos 2t - 337.4⁰ ]

5 - cos(2t) + 12sin(2t)

Is that really what you mean? That constant 5 is going to prevent this from happening. These are both sinusoidal curves:

y = 5 - cos(2t) + 12sin(2t)
Axis: y = 5

y = Acos(2t - θ), where θ is a constant
Axis: y = 0

There can be no way of writing the first expression in the form of the second.