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

Explanation

Given: \(x + y = 90° ... (1)\)

\((\sin x + \sin y)^{2} - 2\sin x \sin y = \sin^{2} x + \sin^{2} y + 2\sin x \sin y - 2\sin x \sin y\)

= \(\sin^{2} x + \sin^{2} y ... (2)\)

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

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