Question

tan^2Θ = ((1-cos(2Θ))/((1+cos(2Θ))
PROVE THE IDENTITY!

Answer 1

tan^2 = sin^2/cos^2 = right hand side
Dat sit

Answer 2

wait HOW is the right side sin^2Θ/cos^2Θ

Answer 3

????

Answer 4

how your nick is music?
tan= sin/cos
so , tan^2 = sin^2/cos^2
I don't know how to answer your How :)

Answer 5

um no how your explanation is right.

Answer 6

how is that equalto the right side

Answer 7

cos (2x) = 1-2sin^2 x--> sin^2x = (1-cos(2x))/2 that's numerator
cos(2x) = 2cos^2-1 do the same to get denominator

Answer 8

yeh. then wut

Answer 9

i get it till there. then what do you do

Answer 10

can you just show me all the steps so its clear, pls?

Answer 11

the proof is done. nothing to say. I am not on the computer. It 's hard to type much moe

Answer 12

I'll gladly help. First off, is this the right side of the original equation?: \[\frac{ 1-\cos^2x }{ 1+\cos^2x }\]

Answer 13

the right side is: 1- cos (2Θ) / (1+cos(2Θ) its cos 2theta

Answer 14

Sorry for the late response.

The double-angle formula states that \[\cos2\theta=\cos^2\theta-\sin^2\theta\]Therefore, the right side can be simplified to \[\frac{ 1-(\cos^2\theta-\sin^2\theta) }{ 1+(\cos^2\theta-\sin^2\theta) }\]And then further to \[\frac{ 1-\cos^2\theta+\sin^2\theta }{ 1+\cos^2\theta-\sin^2\theta }\]Using the pythagorean identity (sin^2x + cos^2x = 1, thus sin^2x = 1 - cos^2x and so on), it can be simplified again to \[\frac{ \sin^2\theta+\sin^2\theta }{ \cos^2\theta+\cos^2\theta }\]Now, we can do simple addition. \[\frac{ 2\sin^2\theta }{ 2\cos^2\theta }\]The 2 in the numerator and the 2 in the denominator can cancel. The ratio identity (also known as reciprocal identity) states that tanx is equal to sinx / cosx. This rule also applies to tan^2, which is equal to sin^2x / cos^2x. We can use this rule to take the expression out of fraction form. \[\tan^2\theta\]Now both sides are equal!