AP EAMCET · Maths · Properties of Triangles
Observe the following statements
(I) In \(\triangle A B C, b \cos ^2 \frac{C}{2}+c \cos ^2 \frac{B}{2}=s\)
(II) In \(\triangle A B C, \cot \frac{A}{2}=\frac{b+c}{2} \Rightarrow B=90^{\circ}\)
Which of the following is correct?
- A Both I and II are true.
- B I is true, II is false.
- C I is false, II is true.
- D Both I and II are false.
Answer & Solution
Correct Answer
(B) I is true, II is false.
Step-by-step Solution
Detailed explanation
(I) Now, \[ \begin{aligned} & , b \cos ^2 \frac{C}{2}+c \cos ^2 \frac{B}{2} \\ & =b \cdot \frac{s(s-c)}{a b}+c \cdot \frac{s(s-b)}{a c} \\ & =\frac{s}{a}(s-c+s-b) \\ & =\frac{s}{a}(2 s-(b+c))=\frac{s}{a} \cdot a \\ & =s \end{aligned} \] \(\therefore\) Statement Ist is true.…
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