Question

sin2x - sqrt(3)cos(2x) > sqrt(2)

[Hint: use formula sin(a-b) = sin(a)cos(b) - cos(a)sin(b)]

Answer 1

Hint2 sin(pi/3) = sqrt(3)/2

Answer 2

In which order do I use these hints? I'm confused on how to break down the given equation so that I can begin to solve for the x values.

Answer 3

try assuming that -sqrt(3)cos(2x) is actually -sin(y)cos(2x) using my hint, then use hint provided to merge them into 1

Answer 4

I'm still a little lost sorry. What does the variable y represent and in your original hint, I don't see any component of it that I can apply (like where is sin(pi/3) or sqrt(3)/2 in the equation provided? )

Thanks replying by the way

Answer 5

ok sin(pi/3) = sqrt(3)/2 as such sqrt(3) = 2sin(pi/3)

therefore you can rewrite -sqrt(3)cos(2x) as -2sin(pi/3)cos(2x) !

Now it somewhat looks like a part of the hint doesnt it? =)

Answer 6

Wow! Headsmack. I can't believe I missed that simple substitution that you were hinting at in your first reply. I'll give this a go again in a bit and make sure to award you Best Response after I've tried it (I assume that is the same as a medal?)

Answer 7

good luck! I am still new to this this place so I have no idea what medals do/represent - but it should be easy from there, if you get stuck again - message away