SOLUTION: I need help with this equation. Thank you. Write 1-csc^2a/1-sin^2a (division-first equation on top of second equation) in simplest form, using only the sine function and/or the

Question 888895: I need help with this equation. Thank you.
Write 1-csc^2a/1-sin^2a (division-first equation on top of second equation) in simplest form, using only the sine function and/or the cosine function. Note any restrictions.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your equation is:

(1-csc^2(a)) / (1-sin^2(a))

since csc(a) = 1/sin(a), your expression becomes:

(1-1/sin^2(a)) / (1-sin^2(a))

place (1-1/sin^2(a)) under a common denominator and you get:

(sin^2(a) - 1) / sin^2(a))

your expression becomes:

(sin^2(a) - 1) / sin^2(a)) / (1 - sin^2(a))

since (sin^2(a) - 1) is equal to -1 * (1 - sin^2(a)), your expression becomes:

(-1 * (1 - sin^2(a)) / sin^2(a)) / (1 - sin^2(a)).

the (1 - sin^2(a)) in the numerator and the (1 - sin^2(a)) in the denominator cancel out and you are left with:

-1 / sin^2(a)

that's your answer.

you can also show it as -csc^2(a).

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