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

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Answer 1 · 2018-01-26T01:24:29

$2sin^2 200^o = 2sin^2 20^o$

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

We can write:

$sin 200^o = sin(180^o + 20^o)$

Using the sum of angles formula:

$sin(A+B)=sinAcosB+cosAsinB$

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:

$sin 200^o = 0 + (-1)sin 20^o = -sin 20^o$

And so:

$2sin^2 200^o = (2)(-sin 20^o)^2 = 2sin^2 20^o$

Express 2sin^2 200^o 2sin^2 200^o in term of 20^o20^o?