If the value of sin theta =12/13 then find the value of 1-cos theta/1+cos theta.
You should recognize the 5-12-13 triangle
if sinØ = 12/13, then
cosØ = 5/13
so (1-cosØ)/(1+cosØ)
= (1-5/13)/(1+5/13)
= (8/13) / (18/13)
= (8/13)(13/18)
=8/18 = 4/9
To find the value of (1 - cos theta) / (1 + cos theta), we need to first determine the value of cos theta.
Given that sin theta = 12/13, we can apply the Pythagorean Identity for sine and cosine, which states that sin^2 theta + cos^2 theta = 1.
Let's solve for cos theta using this identity.
sin^2 theta + cos^2 theta = 1
(12/13)^2 + cos^2 theta = 1
144/169 + cos^2 theta = 1
cos^2 theta = 1 - 144/169
cos^2 theta = 25/169
Now, taking the square root of both sides to determine the value of cos theta:
cos theta = √(25/169)
cos theta = 5/13
Now, substitute the value of cos theta into the expression (1 - cos theta) / (1 + cos theta):
(1 - cos theta) / (1 + cos theta) = (1 - 5/13) / (1 + 5/13)
= (13 - 5) / (13 + 5)
= 8/18
= 4/9
Therefore, the value of (1 - cos theta) / (1 + cos theta) is 4/9.