Use the fundamental identities to simplify the expression.
tan^2 Q / sec^2 Q
sin^2/cos^2 / 1/cos^2 =
sin^2 / cos^2 times cos^2 / 1 =
The cos^2 cancels out so sin^2 is left. Is this correct?
yes
To simplify the expression (tan^2 Q) / (sec^2 Q), we can use the fundamental identities of trigonometry.
The fundamental identities are derived from the Pythagorean identity, which states that sin^2 Q + cos^2 Q = 1. From this identity, we can derive the following identities:
1. tan Q = sin Q / cos Q
2. sec Q = 1 / cos Q
Now let's simplify the expression:
(tan^2 Q) / (sec^2 Q)
Substituting the identities, we have:
(sin^2 Q / cos^2 Q) / (1 / cos^2 Q)
To divide fractions, we multiply the numerator by the reciprocal of the denominator:
(sin^2 Q / cos^2 Q) * (cos^2 Q / 1)
Now, we can cancel out the common factor in the numerator and denominator, which is cos^2 Q:
(sin^2 Q * cos^2 Q) / 1
The cos^2 Q in the numerator cancels out, leaving us with:
sin^2 Q
Therefore, the simplified expression is sin^2 Q. So, your explanation of the simplification is correct.