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3 votes
Write the expression as either the sine, cosine, or tangent of a single angle.

sin 48° cos 15° - cos 48° sin 15°

A. cos 33°

B. cos 63°

C. sin 63°

D. sin 33°

2 Answers

3 votes
The identity that applies here is:
sin(A - B) = sinAcosB - sinBcosA
With A = 48 and B = 15

Thus,
sin(48 - 15)
= sin(33)

The answer is D.
User Clancy Merrick
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8.1k points
4 votes

Answer: Option 'D' is correct.

Explanation:

Since we have given that

sin 48° cos 15° - cos 48° sin 15°

As we know that,


\sin A\cos B-\cos A\sin B=\sin(A-B)

So, we get that


A=48\textdegree\\B=15\textdegree

Now, put it in the above expression.


\sin (A-B)=\sin(48-15)=\sin 33\textdegree

Hence, Option 'D' is correct.

User Mtth
by
8.6k points