Question

Verify the identity algebraically:

cot(a) / (csc(a) - 1) = csc(a) + 1 / cot(a)
A. True
B. False

Answer 1

To verify the given identity, we simplify both sides of the equation and show that they are equal.

Step-by-step explanation:

To verify the identity, we will simplify both sides of the equation and show that they are equal. Starting with the left side, we have:

cot(a) / (csc(a) - 1) = cos(a) / sin(a) / ((1 / sin(a)) - 1) = cos(a) / sin(a) / ((1 - sin(a)) / sin(a)) = cos(a) / (1 - sin(a)).

Now, let's simplify the right side:

csc(a) + 1 / cot(a) = 1 / sin(a) + 1 / (cos(a) / sin(a)) = 1 / sin(a) + sin(a) / cos(a) = cos(a) / sin(a) + sin(a) / cos(a).

Since the left side and right side of the equation are identical, the identity is true.