1. ## Trig Problems

Hey guys, Im really stumped on a revision paper I am doing for homework, if you could help me come to the answer I would appreciate it.

Given that cos x = (3^.5) − 1, find the value of cos 2x in the form a + b(3^.5) ,
where a and b are integers.

Given that
2 cos (y + 30)= 3 sin (y − 30),
find the value of tan y in the form k 3 where k is a rational constant.

2. Originally Posted by GregoryT
Hey guys, Im really stumped on a revision paper I am doing for homework, if you could help me come to the answer I would appreciate it.

Given that cos x = (3^.5) − 1, find the value of cos 2x in the form a + b(3^.5) ,
where a and b are integers.

Given that
2 cos (y + 30)= 3 sin (y − 30),
find the value of tan y in the form k 3 where k is a rational constant.
for the first one use the identity
$\displaystyle \cos(2x)=2\cos^2(x)-1=2(3^{.5}-1)^2-1=....$

for the 2nd use the sum and difference identities for sin and cos

Good luck.

3. Given that cos x = (3^.5) − 1, find the value of cos 2x in the form a + b(3^.5) ,
where a and b are integers.

hint ... $\displaystyle \cos(2x) = 2\cos^2{x} - 1$

Given that
2 cos (y + 30)= 3 sin (y − 30),
find the value of tan y in the form k 3 where k is a rational constant.

hints ...

$\displaystyle \cos(a+b) = \cos{a}\cos{b} - \sin{a}\sin{b}$

$\displaystyle \sin(a-b) = \sin{a}\cos{b} - \cos{a}\sin{b}$

4. Guys, I appreciate the help, although is there any chance you can actually work through the question for me and then let me see if I can grasp that. See, I got as far as you are pointing me but Im resitting after being away from maths for a while. = brain freeze.