Question

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°

Answer 1

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.

Answer 2

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.