^{2}=a

^{2}+b

^{2}-2ab cos θ], you have x = √(2-2cos 2t).

^{2}t = 2-2cos 2t

^{2}t.

^{2}t + cos

^{2}t = 1.

^{2}t - (1 - cos

^{2}t) = cos

^{2}t - sin

^{2}t

^{2}t) = 2 cos

^{2}t - 1.

I want to know how to solve it because i'am having problems

Tutors, sign in to answer this question.

If you don't know things like the addition identity, you can derive the formula by using the law of cosines.

Start with an isosceles triangle with legs of unit length and vertex angle 2t. Let x be the length of the base.

By the law of cosines [c^{2}=a^{2}+b^{2}-2ab cos θ], you have x = √(2-2cos 2t).

Also, the altitude bisects the vertex angle producing two right triangles. Thus x=2 sin t.

Equating gives

2 sin t = √(2-2cos 2t)

4 sin^{2} t = 2-2cos 2t

cos 2t = 1 - 2 sin^{2} t.

We can two other formulas by using the pythagorean identity sin^{2} t + cos^{2} t = 1.

cos 2t = 1 - sin^{2} t - (1 - cos^{2} t) = cos^{2} t - sin^{2} t

and

cos 2t = 1-2(1-cos^{2} t) = 2 cos^{2} t - 1.

Addition identity:

cos (A+B) = CosAcosB - sinAsinB

assuming A=B=t

cos(2t) = cos^2t - sin^2t

also sin^2t + cos^2t = 1

cos^2t = 1- sin^2t

substitite

cos2t = 1- sin^2t - sin^2t

cos2t = 1- 2sin^2t

You can also derive in terms of cos^2t

cos2t = 2cos^2t - 1

:)

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Alain F.

Native speaker for French and Master in Science Grad for Math!

$13.75 per 15 min

View Profile >

Mark A.

Improve your English based on your profession, schedule, and needs.

$10 per 15 min

View Profile >

Kia R.

Learning English Can Be Fun....Let's Do It Together

$10 per 15 min

View Profile >