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How do you verify #csc^2(theta)(1-cos^2(theta))=1#?

Answer 1

Delilah Aguilar

True

#csc^2(theta)*(1-cos^2(theta))=1#

Look for the Pythagorean Identity and solve on the left side.

#1-cos^2(theta) = sin^2(theta)#, this is just a jumbled version of #sin^2x +cos^2x = 1# identity.

Put the new value into practice so that everything is sine on the left.

#1/sin^2(theta)*sin^2(theta)/1 -> sin^2(theta)/sin^2(theta) -> 1#

It seems that all you have to do to identify them in the future is commit their identities to memory.

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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.

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