Question

Express the given expression in terms of sinA: (tan A * cos² A) / sec A.

A) sin A
B) cos A
C) sin² A
D) cos² A

Answer 1

The expression (tan A * cos² A) / sec A simplifies to sin A by using trigonometric identities to replace tan A and sec A with sin A / cos A and 1 / cos A, respectively, and then canceling out the common terms.

Step-by-step explanation:

To express the expression (tan A * cos² A) / sec A in terms of sin A, we can use trigonometric identities.

First, we know that tan A is equal to sin A / cos A and that sec A is equal to 1 / cos A. Plugging these into the expression, we get:
(
(sin A / cos A) * cos² A
) / (
1 / cos A
)
Now we can simplify the expression:

(sin A * cos A * cos A) / (1 / cos A)
= sin A * cos² A * cos A
= sin A * cos A

Since cos A multiplied by itself is cos² A, and we have a cos A in the numerator and denominator, they cancel out, leaving us with:

sin A

Thus, the expression (tan A * cos² A) / sec A simplifies to sin A, which corresponds to option A.