# If #p=cottheta+costheta# and #q=cottheta-costheta#, find the value of #p^2-q^2#?

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Given

Now

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Square both p and q:

Subtract equation [2] from [1]:

The right side of equation [3] is not in the selection list, therefore, we shall try to discover a connection by multiplying p and q:

We know that the right of equation [4] is the difference of two squares:

Make a common denominator:

Combine over the common denominator:

Use the square operator on both sides:

This is one of the selections in the list.

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[ p^2 - q^2 = (cot\theta + cos\theta)^2 - (cot\theta - cos\theta)^2 ] [ = (cot^2\theta + 2cot\theta cos\theta + cos^2\theta) - (cot^2\theta - 2cot\theta cos\theta + cos^2\theta) ] [ = cot^2\theta + 2cot\theta cos\theta + cos^2\theta - cot^2\theta + 2cot\theta cos\theta - cos^2\theta ] [ = 4cot\theta cos\theta ]

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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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- How do I solve this problem?

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