# Express  2sin^2 200^o in term of 20^o?

Jan 26, 2018

$2 {\sin}^{2} {200}^{o} = 2 {\sin}^{2} {20}^{o}$

#### Explanation:

I presume the request is to express the given expression in terms of $\sin {20}^{o}$

We can write:

$\sin {200}^{o} = \sin \left({180}^{o} + {20}^{o}\right)$

Using the sum of angles formula:

$\sin \left(A + B\right) = \sin A \cos B + \cos A \sin B$

We have:

$\sin {200}^{o} = \sin {180}^{o} \cos {20}^{o} + \cos {180}^{o} \sin {20}^{o}$

Now we know that:

$\sin {180}^{o} = 0$ and $\cos {180}^{o} = - 1$

Hence:

$\sin {200}^{o} = 0 + \left(- 1\right) \sin {20}^{o} = - \sin {20}^{o}$

And so:

$2 {\sin}^{2} {200}^{o} = \left(2\right) {\left(- \sin {20}^{o}\right)}^{2} = 2 {\sin}^{2} {20}^{o}$