How do you find the exact functional value sin 110° cos 20° - cos 110° sin 20° using the cosine sum or difference identity?

Answer 1

The expression evaluates to ' 1 '.

In your problem, A=110° and B=20°, so sin(A-B) = sin(110°-20°)= sin (90°)=1. This expression can be evaluated very easily using the formula for sine of difference of two angles, which is sin (A-B) = (sin A cos B - cos A sin B).

However, if you are set on using the cosine sum or difference identity, you can do so by first converting the expression to match the cosine sum or difference formula. You can then move forward as follows:

sin(90°+20°) cos (20°) - cos (90°+20°) sin (20°) = sin(110°) cos(20°) - cos(110°) sin(20°)

In this case, we can apply the formulas cos (90°+x) = {-sin(x)} and sin (90°+x) = cos(x).

It is equal to cos(20°) cos(20°) + sin(20°) sin (20°) - {-sin(20°)} sin (20°).

Furthermore, cos(A-B) = cos A cos B + sin A sin B is known.

equals cos (20°–20°) = cos 0° = 1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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