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

Question

Emery Adkins · Accepted Answer

-1

#1-sec^2t= 1-1/cos^2t# = #(cos^2t-1)/cos^2t# =#-sin^2t/cos^2t# =#-tan^2t# Therefore answer

Abigail Armstrong · Answer

undefined 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 $.

Quinn Anderson · Answer

undefined 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.