Pre-Calculus

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.

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  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.

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