TS EAMCET · Maths · Properties of Triangles
In a \(\triangle A B C\), if \(a+3 b=3 c\), then \(\sin \frac{A}{2}=\)
- A \(\frac{a}{2} \sqrt{\frac{3}{b c}}\)
- B \(\frac{a}{3} \sqrt{\frac{2}{b c}}\)
- C \(\frac{2 a}{3} \sqrt{\frac{1}{b c}}\)
- D \(\frac{a b}{3} \sqrt{\frac{2}{c}}\)
Answer & Solution
Correct Answer
(B) \(\frac{a}{3} \sqrt{\frac{2}{b c}}\)
Step-by-step Solution
Detailed explanation
Since, \(\sin \frac{A}{2}=\sqrt{\frac{(s-b)(s-c)}{b c}}, s=\frac{a+b+c}{2}\) \(=\sqrt{\frac{\frac{a-b+c}{2} \times \frac{a+b-c}{2}}{b c}}\) \(=\sqrt{\frac{\frac{4(c-b)}{2} \times \frac{2(c-b)}{2}}{b c}} \quad[\) as \(a=3(c-b)]\)…
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