Why does
1 - COS2(Squared)
_________________
COS2
= tan2
sloppy way of writing the trig expressions
( when you write tan2, you are asking for the tan(2 radians. What you meant was something like tan^2 Ø
It has to be the sine of something, the cosine of something, or the tangent of something.
anyway .....
(1 - cos^2 Ø)/cos^2 Ø
= sin^2 Ø/cos^2 Ø
= (sinØ/cosØ)^2
= (tanØ)^2
or
tan^2 Ø ............. all by using basic definitions and identities.
Sorry. Don't think I have those keys on this standard keyboard? I could be wrong.
Let me ask. From step 2 to 3 ...
we go from sin / cos squared separately to (sin/cos)2 or times 2 for each? That means the same thing in this case?
We can't just go from step 2 to the last step?
Sin2/Cos2 is tan2?
I'm trying to get this man.
To understand why the expression
(1 - cos^2(x)) / cos^2(x)
is equal to tan^2(x), we need to use the trigonometric identities.
1. The Pythagorean identity states that sin^2(x) + cos^2(x) = 1.
From this identity, we can rearrange it to express sin^2(x) in terms of cos^2(x) as:
sin^2(x) = 1 - cos^2(x)
2. The tangent function is defined as:
tan(x) = sin(x) / cos(x)
Using the previous identity, we can rewrite the numerator of the expression as sin^2(x):
(1 - cos^2(x)) / cos^2(x) = sin^2(x) / cos^2(x)
Now, substituting the definition of the tangent function into this expression:
sin^2(x) / cos^2(x) = (sin(x) / cos(x))^2 = tan^2(x)
Therefore, (1 - cos^2(x)) / cos^2(x) is equal to tan^2(x).