Use the Pythagorean identity sin^2 Θ + cos^2 Θ = 1 to derive the other Pythagorean identities, 1 + tan^2 Θ = sec^2 Θ and 1 + cot^2 Θ = csc^2 Θ. Discuss how to remember these identities and other fundamental identities.

1) 1 + tan² t = sec² t

1 + sin² t / cos² t = 1 / cos² t

(This is because we know that tan x = sin x / cos x and csc x = 1 / cos x)

Then we will multiply both sides of an equation by cos² t

1 * cos² t + sin² t * cos² t / cos² t = 1

cos² t + sin² t = 1 (and we know that it is the identity - true)

2) 1 + cot ² t = csc² t

1 + cos² t / sin² t = 1 / sin² t / · sin² t (multiply both sides by sin² t)

sin² t + cos² t = 1 (true)