Question

Simplify the square root of (1-cos theta)\(1+cos theta)

Answer 1

For this problem, we can use the difference of squares methods, which tells us that

(a−b)(a+b)=a2−b2

Applying this method, we then get

√(1−cosθ)(1+cosθ)=√1−cos2θ

Also note that sin2θ+cos2θ=1→sin2θ=1−cos2θ

Thus we can simplify this even further, giving us

√1−cos2θ=√sin2θ

We have to be careful here, because the root implies that we should have to answers. In fact, if we would have made the mistake of saying that √sin2θ=sinx