Trigonometry Practice Test 2

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Question : 14 of 22

Marks: +1, -0

If sin x + sin y = a and cos x + cos y = b, what is sin x. sin y + cos x. cos y equal to?

a + b - ab
a + b + ab
$a^2 + b^2 - 2$
$({a^2+b^2-2}/2)$
None of these

Solution:

Given,

\sin x + \sin y = a

and

\cos x + \cos y = b

⇒ \sin^2 x + \sin^2 y + 2 \sin x \sin y = a^2

(i)
and

\cos^2 x + \cos^2 y + 2 \cos x \cos y = b^2

(ii)
On adding Eqs. (i) and (ii), we get

(\sin^2 x + \cos^2 x) + (\sin^2 y + \cos^2 y)

+2 (\sin x \sin y + \cos x \cos y) = a^2 + b^2

⇒\sin x \sin y + \cos x \cos y={a^2+b^2-2}/2

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