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

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

A.

1

B.

0

C.

2

D.

-1

Correct answer is A

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