Determinant of Matrix Involving trig Functions

[V0ODO0CH1LD]

Homework Statement

Find the determinant of the matrix {{cos 25°, sin° 65}, {sin 120°, cos 390°}} (sorry, can't latex). {cos 25°, sin° 65} is first row and {sin 120°, cos 390°} is the second one.

Homework Equations

cos(a + b) = (cos a)(cos b) - (sin a) (sin b)

The Attempt at a Solution

I know you can just plug the values in a calculator, but apparently you can solve it by using some trig identities. I also though about using some property of rotation matrices but couldn't find any that fit the problem. Anyway, this is as far as I got:

cos (a + b) = (cos 25°)(cos 390°) - (sin 65°) (sin 120°)

 

[Saitama]

Convert sin(65) into cos(something), rewrite sin(120) as sin(90+30), you can still do one more thing, cos(360+x)=cos(x). Can you start from here?

 

[V0ODO0CH1LD]

Yeah, thanks! I was so caught up thinking on how to simplify the expression I forgot I could just keep on expanding it!