Question

Prove the asked question with all the necessary steps!​

Answer 1

Solving LHS :-

=> (cosx - cosy)² + (sinx - siny)²

=> cos²x + cos²y - 2cosx.cosy + sin²x + sin²y - 2sinx.siny

=> 2 - 2(cosx.cosy + sinx.siny)

=> 2 - 2cos(x - y)

=> 2[1 - cos(x - y)]

=> 2 × 2sin²(x - y)/2

=> 4sin²(x - y)/2

In the given question, there is no condition on x and y. So, you can substitute any angle in place of x and y, the equation has to satisfy that angle. But, if in your question, I substitute x = y = 0, it's not satisfying this substitution. So, the question is wrong in itself. It should be,

(cosx + cosy)² + (sinx - siny)²

= 4cos²(x + y)/2

To solve this, use the similar approach which I've used.

Hope, it'll help you.....