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Prove that,(cos alpha + cos beta)^2 +(sin alpha +sin beta)^2 =4cos^2(alpha -beta/2)

Prove that,(cos alpha + cos beta)^2 +(sin alpha +sin beta)^2 =4cos^2(alpha -beta/2)

Grade:11

2 Answers

Vikas Amritiya
askIITians Faculty 238 Points
one year ago

 

Q n : Prove   that  ,   (cos alpha + cos beta)^2     +
     (sin alpha    +       sin beta )  ^2 =
4cos^2(alpha -beta/2)
 
cos alpha + cos beta)^2 +(sin alpha +sin bet
 
 
Somya
18 Points
one year ago
(cos alpha + cos beta) ² + (sin alpha + sin beta) ² = cos²alpha + sin²alpha + cos²beta + sin² beta +  ( cosalpha *cosbeta + sinalpha* sin beta) 
=2 + 2 ( cos (alpha-beta)) 
2( 2 cos²((alpha - beta/)2)  { 1 + cos 2@ = 2 cos²@/2}
  1. = 4 cos²( (alpha - beta)/2)  = Rhs

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