Strange trigonometric simplification? cos−1(−137)−12π=sin−1137

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Strange trigonometric simplification?  cos−1(−137)−12π=sin−1137

becky4208fj · Accepted Answer

In the first step  cos−1(−137)−12π=(π−cos−1(137))−12π  we are using that for 0≤x≤π  arccos⁡(−θ)=π−arccos⁡θ  which is trivial from the definition of arccos⁡θ dependin for the fact that cos⁡θ=cos⁡(−θ)  For the second step note that for 0≤x≤π2  θ=π2−arccos⁡x⇒sin⁡θ=sin⁡(π2−arccos⁡x)=cos⁡(arccos⁡x)=x  therefore  θ=arcsin⁡x

Strange trigonometric simplification? cos−1(−137)−12π=sin−1137

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