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Simplifying Trig Expressions Using Identities

Q:  Simplify cos4t – sin4t

A:

First thing we gotta notice is that this is a difference of squares.  cos4t is the same as (cos2t)2.  So, we need to use what we know about factoring from algebra to factor this:

cos4t – sin4t can be factored using the difference of squares formula/concept (this just takes practice to see this and realize it):

(cos2t – sin2t)(cos2t + sin2t)

But, now we can use a trig identity because cos2t + sin2t = 1, so plug that in:

(cos2t – sin2t)(cos2t + sin2t)

(cos2t – sin2t)(1) = (cos2t – sin2t)

Now we gotta notice that even though it is simplified a bunch, we have another identity:

(cos2t – sin2t) = cos(2t)

And now we are as simplified as we get.

One thought on “Simplifying Trig Expressions Using Identities

  1. this is over and beyond help full right now, you should come teach at my school. if you can teach math over the internet thats awesome. and i actually understand.

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