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Sum of Trigonometric Ratios in Terms of Their Product

Let x+y bei...

Question

Let $x + y$ being acute and if $sin x . cos y + cos x . sin y = 0$ then the value of $sin x + sin y =$

A

- 1

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B

1

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C

0

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D

none of these

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Solution

The correct option is C $0$
Given,
$sin x . cos y + cos x . sin y = 0$
or, $sin (x + y) = 0$
or, $x + y = 0$ .....(1). [ As $x + y$ being acute]
Now,
$sin x + sin y$
$= sin x + sin (- x)$ [ Using (1)]
$= sin x - sin x$
$= 0$ .

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