Question
Evaluate the following:
$2\sin^230^\circ-3\cos^245^\circ+\tan^260^\circ$
$2\sin^230^\circ-3\cos^245^\circ+\tan^260^\circ$
✓
Answer
$2\sin^230^\circ-3\cos^245^\circ+\tan^260^\circ....(\text{i})$
By trigonometric ratios we have
$\sin30^\circ=\frac{1}{2},\ \cos45^\circ=\frac{1}{\sqrt{2}},\ \tan60^\circ=\sqrt{3}$
By substituing above values in (i) we get
$2\cdot\Big[\frac{1}{2}\Big]^2-3\Big[\frac{1}{\sqrt{2}}\Big]^2+\big[\sqrt{3}\big]^2$
$2\cdot\frac{1}{4}-3\cdot\frac{1}{2}+3$
$\frac{1}{2}-\frac{3}{2}+3\Rightarrow\frac{3}{2}+2=2$
By trigonometric ratios we have
$\sin30^\circ=\frac{1}{2},\ \cos45^\circ=\frac{1}{\sqrt{2}},\ \tan60^\circ=\sqrt{3}$
By substituing above values in (i) we get
$2\cdot\Big[\frac{1}{2}\Big]^2-3\Big[\frac{1}{\sqrt{2}}\Big]^2+\big[\sqrt{3}\big]^2$
$2\cdot\frac{1}{4}-3\cdot\frac{1}{2}+3$
$\frac{1}{2}-\frac{3}{2}+3\Rightarrow\frac{3}{2}+2=2$
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