Expert: Sherman D. - 7/28/2004

Question
How do you go from
(1/sin^2of theta) + (1/cos^2of theta)
to
(cos^2of theta + sin^2of theta)/(sin^2of
theta)(cos^2of theta).  

Answer
This will be really simple to explain.

lets say this

x = sin^2 of theta
y = cos^2 of theta

so

(1/(sin^2 of theta)) + (1/(cos^2 of theta))

becomes

(1/x) + (1/y)

so since "x" and "y" have nothing in common, multiply everything by xy and you get so that you get this as one fraction.

xy((1/x) + (1/y))

(y + x) but don't forget to keep the "xy" denominator, so this gives you

(y + x)/(xy)

don't forget i said that i was using "y" to represent cos^2 of theta, and "x" to represent sin^2 of theta.

so this gives you

(cos^2 of theta + sin^2 of theta)/(sin^2 of theta * cos^2 of theta)

and there you go.