# How do we find the value of #sin^2theta# if #1-cos^2theta = t#?

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To find the value of ( \sin^2\theta ) given that ( 1 - \cos^2\theta = t ), we can use the Pythagorean identity for trigonometric functions. The Pythagorean identity for sine and cosine is:

[ \sin^2\theta + \cos^2\theta = 1 ]

Rearrange the given equation to isolate ( \cos^2\theta ):

[ \cos^2\theta = 1 - t ]

Now substitute this expression for ( \cos^2\theta ) into the Pythagorean identity:

[ \sin^2\theta + (1 - t) = 1 ]

Simplify the equation:

[ \sin^2\theta = t ]

So, the value of ( \sin^2\theta ) is equal to ( t ).

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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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