00:02
Okay, in this video we're going to work on using some trig identities.
00:07
The expression that we're given is 4 sine to the 4x, and we are asked to reduce this down using the power reducing formulas so that we don't have any trig functions with a power greater than 1.
00:25
So let's look at our power reducing formulas.
00:29
We have sine squared x is equal to 1 minus cosine of 2x over 2, and cosine squared x is equal to 1 plus cosine of 2x over 2.
00:49
Now there is one for tangent squared, but we don't need that.
00:53
We only have sign here.
00:54
I'm going to rewrite this as 4 times the sine.
01:00
Squared of x times the sine squared of x.
01:04
You can also do sine squared squared squared, but i think this way, at least for me, it's a little more straightforward.
01:12
So we can use this power reducing formula twice.
01:17
We have one here, and we have one here.
01:20
So this is going to be equal to four times one minus cosine of 2x over 2 times 1 minus cosine of 2x over 2.
01:40
And so that's equal to 4.
01:42
And you'll notice that here we have 2 times 2, so i'm going to end up with a fraction all over 4.
01:49
And for this 1 minus cosine 2x, 1 minus cosine 2x, i'm just going to foil that out.
01:56
I'm going to get 1 minus 2 cosine of 2x plus 1 minus 2x ,000.
02:04
Cosine squared of 2x.
02:08
And then you'll notice that these fours will cancel...