If x + y = 90 simplify (sinx + siny)2−2sinxsiny

If x + y = 90 simplify (sinx + siny)2−2sinxsiny

Correct Answer: Option A

Explanation

Given: (x + y = 90° … (1))

((sin x + sin y)^{2} – 2sin x sin y = sin^{2} x + sin^{2} y + 2sin x sin y – 2sin x sin y)

= (sin^{2} x + sin^{2} y … (2))

Recall: (sin x = cos (90 – x) … (a))

From (1), (y = 90 – x … (b))

Putting (a) and (b) in (2), we have

(sin^{2} x + sin^{2} y equiv cos^{2} (90 – x) + sin^{2} (90 – x))

= 1

There is an explanation video available below.