Trig Help?!

[Reece]

Verify Each Trigonometric Identity

1.
(sec x/sin x) - (sin x/cos x) = cot x

2.
sin (360° + x) = sin x

3.
(cos x) - (cos x/1 - tan x) = (sinxcosx/sin x - cos x)



Solve Each Trigonometric Equation

4.
tan 2x - √3 = 0

5.
4cos² x - 3 = 0

Can anyone help with these?

[Kurtz]

Hey, Reece.
These are Trig Identities, correct?

4. tan 2x - √3 = 0

Solution:
Possible intermediate steps:
tan(2 x)-sqrt(3) = 0
Add sqrt(3) to both sides:
tan(2 x) = sqrt(3)
Take the inverse tangent of both sides:
2 x = pi/3
Divide both sides by 2:
x = pi/6



5.4cos² x - 3 = 0

Solution:
Possible intermediate steps:
4 cos^2(x)-3 = 0
Add 3 to both sides:
4 cos^2(x) = 3
Divide both sides by 4:
cos^2(x) = 3/4
Take the square root of both sides:
cos(x) = -sqrt(3)/2 or cos(x) = sqrt(3)/2
Take the inverse cosine of both sides:
x = (5 pi)/6 or cos(x) = sqrt(3)/2
Take the inverse cosine of both sides:
x = (5 pi)/6 or x = pi/6

Hope this helps,
Regards
Kurtz.