Math Help - Help with sines?

1. Help with sines?

Obviously, a calculator cannot be used.

1) cos^-1(tan(37.5))

2) cos80deg(cos20deg) + sin80deg(sin20deg)

3) cos(tan^-1(-sqroot3))

4) The domain and range of tan(cos^-1(x/2)(2))

5) A formula for cos(30) in terms of cosX alone.

6) The period of 3cos (5(pi)x + 7)

Thanks and rep to anyone that solves any of these.

2. Originally Posted by theqwertykid

3) cos(tan^-1(-sqroot3))

$\tan(60^{\circ})=\sqrt{3},$

so:

$\tan(120^{\circ})=-\sqrt{3}$

also:

$\tan(300^{\circ})=-\sqrt{3}$

CB