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T-Ratios of Some Particular Angles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsT-Ratios of Some Particular Angles5 Marks
Question
Evaluate the following:
Using the formula, $\sin\text{A}=\sqrt{\frac{1-\cos2\text{A}}{2}},$ Find the value of $\sin30^\circ,$ it being given that $\cos60^\circ=\frac{1}{2}.$
✓

Answer

$\text{A}=30^\circ$
$\Rightarrow2\text{A}=2\times30^\circ=60^\circ$
By substiting the value of the given T-ratio, we get:
$\sin\text{A}=\sqrt{\frac{1-\cos2\text{A}}{2}}$
$\Rightarrow\sin30^\circ=\sqrt{\frac{1-\cos60^\circ}{2}}$
$\sqrt{\frac{1-\frac12}{2}}=\sqrt{\frac{\frac12}{2}}$
$=\sqrt{\frac14}=\frac12$
$\therefore\ \sin30^\circ=\frac12$

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