AP EAMCET · Maths · Properties of Triangles
In any triangle \(A B C\) \(a \cdot \cos ^2 \frac{A}{2}+b \cdot \cos ^2 \frac{B}{2}+c \cdot \cos ^2 \frac{C}{2}=\)
- A \(\frac{\Delta}{R}\)
- B \(s+\frac{\Delta}{R}\)
- C \(2 s+\frac{\Delta}{R}\)
- D \(\frac{\Delta s}{R}\)
Answer & Solution
Correct Answer
(B) \(s+\frac{\Delta}{R}\)
Step-by-step Solution
Detailed explanation
\(a \cdot \cos ^2 \frac{A}{2}+b \cdot \cos ^2 \frac{B}{2}+c \cdot \cos ^2 \frac{C}{2}\) \(= a \left(\frac{1 + \cos A}{2}\right) + b \left(\frac{1 + \cos B}{2}\right) + c \left(\frac{1 + \cos C}{2}\right)\) \(= \frac{a+b+c}{2} + \frac{1}{2} (a \cos A + b \cos B + c \cos C)\)…
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