Question
Evaluate the following:
$2\cos^260^\circ+3\sin^245^\circ-3\sin^230^\circ+2\cos^290^\circ$
$2\cos^260^\circ+3\sin^245^\circ-3\sin^230^\circ+2\cos^290^\circ$
✓
Answer
On substituting values of various T-ratious, we get:
$2\cos^260^\circ+3\sin^245^\circ-3\sin^230^\circ+2\cos^290^\circ$
$=2\times\Big(\frac12\Big)^2+3\times\Big(\frac{1}{\sqrt{2}}\Big)^2-3\times\Big(\frac12\Big)^2+2\times(0)^2$
$=2\times\frac14+3\times\frac12-3\times\frac14+0$
$=\Big(\frac12+\frac32-\frac34\Big)=\Big(\frac{2+6-3}{4}\Big)=\frac54$
$2\cos^260^\circ+3\sin^245^\circ-3\sin^230^\circ+2\cos^290^\circ$
$=2\times\Big(\frac12\Big)^2+3\times\Big(\frac{1}{\sqrt{2}}\Big)^2-3\times\Big(\frac12\Big)^2+2\times(0)^2$
$=2\times\frac14+3\times\frac12-3\times\frac14+0$
$=\Big(\frac12+\frac32-\frac34\Big)=\Big(\frac{2+6-3}{4}\Big)=\frac54$
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