Trigonometry Practice Test 1

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Question : 23 of 40

Marks: +1, -0

If

A=\cos x\cos y,

B=\sin x\sin y

and

C=\sin^2x+\sin^2y,

what is the value of

A^2-B^2?

C
1 - C
1 + C
C - 1
None of these

Solution:

Given,

A=\cos x\cos y,

B=\sin x\sin y

and

c=\sin^2x+\sin^2y,

Now,

A^2-B^2

=\cos^2x\cos^2y-\sin^2x\sin^2y

=(1-\sin^2x)(1-\sin^2y)-\sin^2x\sin^2y

=1-\sin^2x-\sin^2y+\sin^2y\sin^2x-\sin^2x\sin^2y

=1-(\sin^2x+\sin^2y)

=1-C

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