Question

This question has me stuck. 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.

Answer 1

for the first one:

sin^2 Ø + cos^2 Ø = 1
divide each term by cos^2 Ø
sin^2 Ø/cos^2 Ø + cos^2 Ø/cos^2 Ø = 1/cos^2 Ø
tan^2 Ø + 1 = sec^2 Ø, (since 1/cosx = secx)

do the 2nd by dividing each term by sin^2 Ø

How to remember them?
Just memorize them.