Question

Which expression is equivalent to cos(1.4x) − cos(0.6x)?

A. -2sin x sin(0.4x)

B. 2sin x sin(0.4x)

C. -2cos x cos(0.4x)

D. 2cos x cos(0.4x)

Answer 1

A. -2sin x sin(0.4x)

Explanation:

At x=0, the given expression evaluates to zero.

For x near zero, the given expression is slightly negative. You know this because cos(1.4x) decreases faster than cos(0.6x), so their difference will be negative.

Of the answer choices, you can eliminate C and D because they are not zero at x=0. You can eliminate choice B, because it is positive for values of x near zero. The only viable choice is A: -2sin(x)sin(0.4x)

Answer 2

A. -2sin(x)sin(0.4x)

Explanation:

At x=0, the given expression evaluates to zero.

For x near zero, the given expression is slightly negative. You know this because cos(1.4x) decreases faster than cos(0.6x), so their difference will be negative.

Of the answer choices, you can eliminate C and D because they are not zero at x=0. You can eliminate choice B, because it is positive for values of x near zero. The only viable choice is A:

-2sin(x)sin(0.4x)

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Of course, a graphing calculator can help you figure this out. See the attachment. The given expression is plotted using a solid red line; the answer choice A is plotted using blue dots.