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

Question

1594 views around the world

You can reuse this answer
Creative Commons License

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 #