Question

The value of (cos α + cos β)² + (sin α + sin β)² is ______.

विकल्प

• `2 cos^2 ((α - β)/2)`

• `4 cos^2 ((α - β)/2)`

• `4 sin^2 ((α - β)/2)`

• `2 sin^2 ((α - β)/2)`

Answer 1

The value of (cos α + cos β)² + (sin α + sin β)² is `underlinebb(4  cos^2 ((α - β)/2))`.

Explanation:

We have, (cos α + cos β)² + (sin α + sin β)² 

= cos² α + cos² β + 2 cos α cos β + sin² α + sin² β + 2 sin α sin β

= (cos² α + sin² α) + (cos² β + sin² β) + 2[cos α cos β + sin α sin β]

= 1 + 1 + 2[cos (α – β)]

= 2[1 + cos (α – β)]

= `2[2 cos^2 ((α - β)/2)]`

= `4 cos^2 ((α - β)/2)`