Question

prove the identity that (tan^2 x) - (sin^2 x) = (tan^2 x)(sin^2 x)

Answer 1

candy020202 are you here?

Answer 2

yeah

Answer 3

so i want to say. i have solved this and its proof is too long. approx 3 pages. so..

Answer 4

i dont think it should be that long though because the other problems only take up like 1/8 of a page

Answer 5

yes. but it is.. therefore anyone didn't touch that. i think so.

Answer 6

do you have windows 7?

Answer 7

no

Answer 8

ok which window?

Answer 9

what?

Answer 10

ok wait. i do something.

Answer 11

its ok i can figure it out though.

Answer 12

gracias

Answer 13

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

Replace tanx with an equivalent expression (sin^(2)x)/(cos^(2)x) using the fundamental identities.
(sin^(2)x)/(cos^(2)x)-sin^(2)x

To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is cosx^(2). Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(sin^(2)x)/(cos^(2)x)-sin^(2)x*(cos^(2)x)/(cos^(2)x)

Complete the multiplication to produce a denominator of cosx^(2) in each expression.
(sin^(2)x)/(cos^(2)x)-(sin^(2)xcos^(2)x)/(cos^(2)x)

Combine the numerators of all expressions that have common denominators.
(sin^(2)x-sin^(2)xcos^(2)x)/(cos^(2)x)

Factor out the GCF of sinx^(2) from each term in the polynomial.
(sin^(2)x(1)+sin^(2)x(-cos^(2)x))/(cos^(2)x)

Factor out the GCF of sinx^(2) from sinx^(2)-sinx^(2)cosx^(2).
(sin^(2)x(1-cos^(2)x))/(cos^(2)x)

Replace 1-cos^(2)x with sin^(2)x using the identity sin^(2)(x)+cos^(2)(x)=1.
(sin^(2)x(sin^(2)x))/(cos^(2)x)

Multiply sinx^(2) by sinx^(2) in the numerator.
(sin^(2)x*sin^(2)x)/(cos^(2)x)

Multiply sinx^(2) by sinx^(2) to get sinx^(4).
(sin^(4)x)/(cos^(2)x)

To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is cosx^(2). Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(sin^(2)x)/(cos^(2)x)-sin^(2)x*(cos^(2)x)/(cos^(2)x)

Complete the multiplication to produce a denominator of cosx^(2) in each expression.
(sin^(2)x)/(cos^(2)x)-(sin^(2)xcos^(2)x)/(cos^(2)x)

Combine the numerators of all expressions that have common denominators.
(sin^(2)x-sin^(2)xcos^(2)x)/(cos^(2)x)

Factor out the GCF of sinx^(2) from each term in the polynomial.
(sin^(2)x(1)+sin^(2)x(-cos^(2)x))/(cos^(2)x)

Factor out the GCF of sinx^(2) from sinx^(2)-sinx^(2)cosx^(2).
(sin^(2)x(1-cos^(2)x))/(cos^(2)x)

Replace 1-cos^(2)x with sin^(2)x using the identity sin^(2)(x)+cos^(2)(x)=1.
(sin^(2)x(sin^(2)x))/(cos^(2)x)

Multiply sinx^(2) by sinx^(2) in the numerator.
(sin^(2)x*sin^(2)x)/(cos^(2)x)

Multiply sinx^(2) by sinx^(2) to get sinx^(4).
(sin^(4)x)/(cos^(2)x)

Rewrite the expression using the (sinx)/(cosx)=tanx identity.
sin^(2)xtan^(2)x