Is 1cos2θ=sinθ true?

1 Answer
May 24, 2017

Sometimes

Explanation:

It helps to know some Pythagorean identities:

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If we solve for the first one, we can see that sin2x=1cos2x. Substitute this inside the square root. Note that x is just a dummy variable, we could use θ instead:

sin2θ=sinθ

Simplify the left side:

±sinθ=sinθ

Since sinθ is an odd function, we can only conclude that sinθ=sinθ, and as such, 1cos2x=sinθ when θ is negative, for example.