Question

How is √ [2A² (1 + cosθ)] = √ [4A² cos² θ/2] ?

Answer 1

Solution :

By applying the identity of the half angle identity.

cos^2( θ/2 )= 1 + cosθ / 2

=> 1 + cosθ = 2cos^2( θ/2 )

By putting the value of (1 + cosθ) in √ [2A² (1 + cosθ)]

Here, the value of (1 + cosθ) is 2cos^2( θ/2 ).

Now, put this 2cos^2( θ/2 ) in the place of (1 + cosθ)

=> √ [2A² (1 + cosθ)] = √ [4A² (cos² θ/2)]

=> √ [2A² (1 + cosθ)] = √ [4A² cos² θ/2]

.°. √ [2A² (1 + cosθ)] = √ [4A² cos² θ/2]

Hence, it is proved.