Question

Cot2(t) − cos2(t) = cot2(t) cos2(t).
A - True
B - False.

Answer 1

The statement is false. The equation is not true.

Step-by-step explanation:

This statement is false.

To prove this, let's simplify both sides of the equation and see if they are equal. We will use the trigonometric identities provided in the reference.

Starting with the left side of the equation:

cot^2(t) - cos^2(t)

Using the identity cot^2(t) - 1 = cos^2(t), we can rewrite the left side as:

cos^2(t) - cos^2(t)

Which simplifies to:

0

Now let's look at the right side of the equation:

cot^2(t)cos^2(t)

Using the identity cot^2(t) = 1/cos^2(t), we can rewrite the right side as:

1 - cos^2(t)

Which simplifies to:

1 - cos^2(t)

Since the left side simplifies to 0 and the right side simplifies to 1 - cos^2(t), which is not equal to 0, the equation is false.

Therefore, the correct answer is B - False.