Question

Find the outcome of: cos(pi/4+pi/3)

Irrational numbers
ANSWERED
asked 2021-01-28
Find the outcome of:
\(\displaystyle{\cos{{\left(\frac{\pi}{{4}}+\frac{\pi}{{3}}\right)}}}\)

Answers (1)

2021-01-29
\(\displaystyle{\cos{{\left({A}+{B}\right)}}}={\cos{{A}}}{\cos{{B}}}-{\sin{{A}}}{\sin{{B}}}\)
\(\displaystyle{\cos{{\left(\frac{\pi}{{4}}+\frac{\pi}{{3}}\right)}}}={\cos{{\left(\frac{\pi}{{4}}\right)}}}{\cos{{\left(\frac{\pi}{{3}}\right)}}}-{\sin{{\left(\frac{\pi}{{4}}\right)}}}{\sin{{\left(\frac{\pi}{{3}}\right)}}}\)
\(\displaystyle=\frac{\sqrt{{2}}}{{2}}\times\frac{{1}}{{2}}-\frac{\sqrt{{2}}}{{2}}\times\frac{\sqrt{{3}}}{{2}}\)
\(\displaystyle=\frac{\sqrt{{2}}}{{4}}-\frac{\sqrt{{6}}}{{4}}\)
\(\displaystyle=\frac{{\sqrt{{2}}-\sqrt{{6}}}}{{4}}\)
The answer:
\(\displaystyle{\cos{{\left(\frac{\pi}{{4}}+\frac{\pi}{{3}}\right)}}}=\frac{{\sqrt{{2}}-\sqrt{{6}}}}{{4}}\)
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