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| Math Central | Quandaries & Queries |
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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, Alex
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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,
Stephen.
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