First slide

Properties of triangles

Question

$A_{1} A_{2} A_{2} A_{4} A_{5} A_{6} A_{7} are the vertices of a regular septagon, inscribed in a circle of$
$radius 1 & |A_{1} A_{2}| \cdot |A_{1} A_{3}| + |A_{1} A_{3}| \cdot |A_{1} A_{4}| + |A_{1} A_{4}| \cdot |A_{1} A_{5}| + |A_{1} A_{5}| \cdot |A_{1} A_{6}| + |A_{1} A_{6}| \cdot |A_{1} A_{7}| = acos (\frac{π}{7}) then [\frac{a}{3}] =$ $([.] denotes G I F)$

Difficult

Solution

Given equation
$\begin{array}{l} 4 \{\sin \frac{π}{7} \sin \frac{2 π}{7} + \sin \frac{2 π}{7} \sin \frac{3 π}{7} + \sin \frac{3 π}{7} \sin \frac{4 π}{7} + \sin \frac{4 π}{7} \sin \frac{5 π}{7} + \sin \frac{5 π}{7} \sin \frac{6 π}{7}\} \\ = 2 \{5 \cos \frac{π}{7} - [\cos \frac{3 π}{7} + \cos \frac{5 π}{7} + \cos \frac{7 π}{7} + \cos \frac{9 π}{7} + \cos \frac{11 π}{7}]\} \\ = 10 \cos \frac{π}{7} - 2 \{\frac{- 2 \cdot \sin \frac{π}{7} \cos \frac{π}{7}}{\sin \frac{π}{7}}\} \\ = 14 \cos \frac{π}{7} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App