Expert: Sherman D. - 11/13/2006

Question
I'm having a problem proving this identity.

tan(sqaured)*sin(squared)=tan(squared)+cos(sqaured)-1

Answer
(tan(x))^2 * (sin(x))^2 = (tan(x))^2 + (cos(x))^2 - 1
tan(x)^2 * sin(x)^2 = tan(x)^2 - 1 + cos(x)^2
tan(x)^2 * sin(x)^2 = tan(x)^2 + (-1 + cos(x)^2)
tan(x)^2 * sin(x)^2 = tan(x)^2 - (1 - cos(x)^2)

sin(x)^2 = 1 - cos(x)^2
tan(x)^2 = (sin(x)/cos(x))^2

tan(x)^2 * sin(x)^2 = (sin(x)^2 / cos(x)^2) - sin(x)^2

tan(x)^2 * sin(x)^2 = (sin(x)^2 - (sin(x)^2 * cos(x)^2)/(cos(x)^2

tan(x)^2 * sin(x)^2 = ((sin(x)^2)(1 - cos(x)^2))/(cos(x)^2)

tan(x)^2 * sin(x)^2 = (sin(x)^2 / cos(x)^2) * (1 - cos(x)^2)

Using what i told you from above

tan(x)^2 * sin(x)^2 = tan(x)^2 * sin(x)^2

You can find more info at

www.math.com/tables/trig/identities.htm