Question

prove tht sin2theta+ cos2theta=1

Answer 1

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Let (C) be a unit circle, and M∈(C).
Also, we will denote ∠IOM as θ (see the diagram).
From the unit circle definition, the coordinates of the point M are (cosθ,sinθ).
And so, ¯OC is cosθ and ¯OS is sinθ. Therefore, OM=√¯OC2+¯OS2=√cos2θ+sin2θ.

Since M lies in the unit circle, OM is the radius of that circle, and by definition, this radius is equal to 1.
It immediately follows that:cos2θ+sin2θ=1

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Answer 2

Answer: actually we don't need to prove it is a formula