Question

सिद्ध कीजिए: `(cos x - cosy)^2 + (sin x - sin y)^2 = 4 sin^2  (x - y)/2`

Answer 1

बायाँ पक्ष = (cos x – cos y)² + (sin x – sin y)²

= `( -2sin  (x + y)/2  sin  (x - y)/2)^2 + (2cos  (x + y)/2  sin  (x -  y)/2)^2`

=  `4sin^2  (x +y)/2  sin^2  (x - y)/2 + 4cos^2  (x +y)/2  sin^2  (x - y)/2`

= `4sin^2 (x -y) [ sin^2  (x + y)/2 + cos^2  (x +y)/2]`

= `4sin^2  (x - y)/2`  `[∵ sin^2  (x  + y)/2 + cos^2  (x +y)/2 = 1]`

= दायाँ पक्ष।