Question

Given the angles of a triangle are in A.P with a common difference equal to the smallest angle. Find the value of cosA X cosB X cosC, where A, B and C are the angles of the triangle.

• A. 0
• B. (1/2)
• C.
  
• D.
  

Answer 1

The correct option is A

0

Let A be the smallest angle,

The other angles will be 2A, 3A.

Sum of angles in a triangle =${180}^{\circ }$

$A+2A+3A={180}^{\circ }$

$A={30}^{\circ }$

The other two angles will be ${60}^{\circ }$ and ${90}^{\circ }$

$cos{90}^{\circ }=0$

So, cosA X cosB X cosC = 0.