Question

sin(2cos^-1*((sqrt2)/2)

Trigonometric Functions
ANSWERED
asked 2021-06-04

\(\displaystyle{\sin{{\left({2}{{\cos}^{{-{{1}}}}\times}{\left(\frac{{\sqrt{{2}}}}{{2}}\right)}\right)}}}\)

Answers (1)

2021-06-05

We are given: \(\displaystyle{\sin{{\left({2}{{\cos}^{{-{{1}}}}\times{\left(\frac{{\sqrt{{2}}}}{{2}}\right)}}\right)}}}\)
Since \(\displaystyle{\cos{{45}}}°=\frac{{\sqrt{{2}}}}{{2}}\), then \(\displaystyle{{\cos}^{{-{{1}}}}{\left(\frac{{\sqrt{{2}}}}{{2}}\right)}}={45}°\)

so: \(=\sin(2 \times 45^{\circ})=\sin90^{\circ}=1\)

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