Question

Prove the following: 1/1 + tan A = cot A/1 + cot A

a. 1 + tan A/1 = cot A
b. 1/1 + tan A = 1/1 + cot A
c. 1/1 + tan A = cot A
d. 1/1 + tan A = cot A/cot A + 1

Answer 1

To prove the equation 1/1 + tan A = cot A/1 + cot A, we simplify both sides and substitute cot A with 1/tan A to show that they are equal.

Step-by-step explanation:

To prove the equation: 1/1 + tan A = cot A/1 + cot A

We can start by simplifying the left side:

1/1 + tan A = 1 + tan A

Next, let's simplify the right side:

cot A/1 + cot A = 1/cot A + cot A

Now, we can simplify the equation:

1 + tan A = 1/cot A + cot A

Since cot A = 1/tan A, we can substitute:

1 + tan A = 1/(1/tan A) + 1/tan A

1 + tan A = tan A + 1/tan A

Now, we can see that both sides are equal, so the equation is proved.

The correct answer is: a. 1 + tan A/1 = cot A