Solveeit Logo
Login

Question

Question: cos2\(\frac{A}{2}\)+ cos2\(\frac{B}{2}\)+ cos2\(\frac{C}{2}\)=...

cos2A2\frac{A}{2}+ cos2B2\frac{B}{2}+ cos2C2\frac{C}{2}=

A

2 – rR\frac{r}{R}

B

2 –r2R\frac{r}{2R}

C

2 + r2R\frac{r}{2R}

D

None of these

Answer

2 + r2R\frac{r}{2R}

Explanation

Solution

cos2 A2\frac{A}{2}+ cos2 B2\frac{B}{2}+ cos2 C2\frac{C}{2}

= 12\frac{1}{2} [1 + cos A + 1 + cos B + 1 + cos C]

=32\frac{3}{2}+12\frac{1}{2}+r2R\frac{r}{2R} [since cosA + cosB + cosC = 1+ rR\frac{r}{R}]

= 2 + r2R\frac{r}{2R}