Math CentralQuandaries & Queries


Question from Alex, a student:

Use the identities tan_=sin_/cos_  and/or sin*_+cos*_=1 to simplify 1-cos*_

I'm sorry if this is hard to understand. I don't know how to make a small raised 2 I used * to mean squared. I used _ for the symbol that looks like a 0 with a line through it.

Thanks for any help you can give me,


Hi Alex.

The symbol that looks like a 0 with a line through it is the greek letter "theta": θ. It is just a variable, you could as easily just call it x instead. For exponents, we usually type ^ (carat) in front.

Anyway, the identity you want is the second one: sin2θ + cos2θ = 1.

If we replace sin2θ with the variable a, and cos2θ with the variable b, then this is a + b = 1, and the question becomes: simplify 1 - b.

Well, a = 1 - b. We can just subtract b from both sides of the equation. And what is a? it is sin2θ.

So 1 - cos2θ = sin2θ.

You see Alex, we can just use the usual rules of equations to solve the problem, the presence of the trig functions doesn't change that.

Hope this helps,

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