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Trigonometric Ratios of Some Particular Angles — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsTrigonometric Ratios of Some Particular Angles3 Marks
Question
Evaluate the following:
Using the formula, $\cos\text{A}=\sqrt{\frac{1+\cos2\text{A}}{2}},$ Find the value of $\cos30^\circ,$ it being given that $\cos60^\circ=\frac12.$
✓

Answer

$\text{A}=30^\circ$
$\Rightarrow2\text{A}=2\times30^\circ=60^\circ$
By substiting the value of the given T-ratio, we get:
$\cos\text{A}=\sqrt{\frac{1+\cos2\text{A}}{2}}$
$\Rightarrow\cos30^\circ=\sqrt{\frac{1+\cos60^\circ}{2}}$
$\sqrt{\frac{1+\frac12}{2}}=\sqrt{\frac{\frac32}{2}}$
$=\sqrt{\frac34}=\frac{\sqrt{3}}{2}$
$\therefore\ \cos30^\circ=\frac{\sqrt{3}}{2}$

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