Answer:
See Below.
Step-by-step explanation:
Problem 1)
We want to verify that:
Note that cot(x) = cos(x) / sin(x). Hence:
Multiply:
Recall that Pythagorean Identity: sin²(x) + cos²(x) = 1 or cos²(x) = 1 - sin²(x). Substitute:
Split:
Simplify:
Problem 2)
We want to verify that:
Square:
Convert csc(x) to 1 / sin(x) and cot(x) to cos(x) / sin(x). Thus:
Factor out the sin²(x) from the denominator:
Factor (perfect square trinomial):
Using the Pythagorean Identity, we know that sin²(x) = 1 - cos²(x). Hence:
Factor (difference of two squares):
Factor out a negative from the first factor in the denominator:
Cancel:
Distribute the negative into the numerator. Therefore: