Step-by-step explanation:
Let's take the RHS,
we've,
(Cosa/2 - sina/2)
(Cosa/2 + sina/2)
Let's Rationalise the Denominator.
we get,
(Cosa/2 - sina/2)^2
(cosa/2)^2 - (sina/2)^2
The numerator is in form of (a-b)^2 and the denominator is in form of a^2-b^2. Now,
By formula,
(Cosa/2)^2 -2cosa/2.sina/2 + (sina/2)^2
cosa
Here I substituted Cosa in place of (Cosa/2)^2 - (sina/2)^2 because it's the formula of cosa in sub multiple angle form.
In the numerator,
(sina/2)^2 + (Cosa/2)^2 =1.........( by formula)
so we have,
1 - 2sina/2.cosa/2
Cosa
1 - sina {because 2sina/2.cosa/2=sina)
Cosa
LHS proved.
Thank You.
