Question

1-sina/cosa=cosa/2-sina/2÷cosa/2+sina/2​

Answer 1

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.