# How do you simplify the expression #tan^2t/(1-sec^2t)#?

-1

Therefore answer

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To simplify the expression ( \frac{\tan^2(t)}{1 - \sec^2(t)} ), you can use trigonometric identities.

[ \tan^2(t) = \sec^2(t) - 1 ]

Substituting this identity into the expression, we get:

[ \frac{\sec^2(t) - 1}{1 - \sec^2(t)} ]

Now, we can simplify by factoring out a negative from the denominator:

[ \frac{\sec^2(t) - 1}{- (\sec^2(t) - 1)} ]

Finally, simplifying further, we have:

[ \frac{1}{-1} = -1 ]

Therefore, the simplified expression is ( -1 ).

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To simplify the expression tan^2(t)/(1 - sec^2(t)), you can start by expressing sec^2(t) as 1 + tan^2(t), using the identity sec^2(t) = 1 + tan^2(t). Then substitute this expression into the denominator of the original expression. After substitution, you will have tan^2(t) / (1 - (1 + tan^2(t))). Simplify further by distributing the negative sign inside the parentheses and combining like terms. This will result in tan^2(t) / (-tan^2(t)). Finally, cancel out the common factor of tan^2(t) in the numerator and denominator to get -1 as the simplified expression.

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