Question
Evaluate the following:
$\cos^230^\circ+\cos^245^\circ+\cos^260^\circ+\cos^290^\circ$
$\cos^230^\circ+\cos^245^\circ+\cos^260^\circ+\cos^290^\circ$
✓
Answer
$\cos^230^\circ+\cos^245^\circ+\cos^260^\circ+\cos^290^\circ=\Big(\frac{\sqrt3}{2}\Big)^2+\Big(\frac{1}{\sqrt2}\Big)^2+\Big(\frac{1}{2}\Big)^2+(0)^2$
$=\frac{3}{4}+\frac{1}{2}+\frac{1}{4}+0$
$=\frac{3+2+1}{4}$
$=\frac{6}{4}=\frac{3}{2}$
$=\frac{3}{4}+\frac{1}{2}+\frac{1}{4}+0$
$=\frac{3+2+1}{4}$
$=\frac{6}{4}=\frac{3}{2}$
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