Tan x Cot - Cos² = Sin²?

Question

Using Trigonometric Identities.

has to equal Sin²

Answer 1

tan(x)cot(x) - cos²(x) = sin²(x)

tan(x)cot(x) - cos²(x)
= tan(x)[1/tan(x)] - cos²(x)
= 1 - cos²(x)

Recall
cos²(x) + sin²(x) = 1

So 1 - cos²(x) = sin²(x)

Answer 2

I assume that your equation is written like this
Tan x Cot x - Cos^2 x = Sin^2 x
From Identities Cot x = 1 / Tan x ( Substitute in the equation)
Tan x ( 1/ Tan x) - Cos^2 x = Sin^2 x ( The tangents will cancell)
1-Cos^2x = Sin^2 x .. Is an Identity from Sin^2 x + Cos^2 x = 1

Answer 3

verify here id: (cot(x) tan(x)-sin(x)^2)/(cot(x) sin(x)) = cos(x) Write cotangent as cosine/sine and tangent as sine/cosine: ((cos(x))/(sin(x)) (sin(x))/(cos(x))-sin(x)^2)/((cos(x))/(s... sin(x)) = ^?cos(x) (((cos(x))/(sin(x))) ((sin(x))/(cos(x)))-sin(x)^2)/(((cos(x))... sin(x)) = (a million-sin(x)^2)/(cos(x)): (a million-sin(x)^2)/(cos(x)) = ^?cos(x) Multiply the two facets via cos(x): a million-sin(x)^2 = ^?cos(x)^2 sin(x)^2 = a million/2 (a million-cos(2 x)): a million-(a million-cos(2 x))/2 = ^?cos(x)^2 (a million-cos(2 x))/2 = a million/2-a million/2 cos(2 x): a million-a million/2-(cos(2 x))/(2) = ^?cos(x)^2 -(a million/2-(cos(2 x))/(2)) = a million/2 cos(2 x)-a million/2: a million+(cos(2 x))/2-a million/2 = ^?cos(x)^2 a million-a million/2+(cos(2 x))/2 = a million/2+a million/2 cos(2 x): a million/2+(cos(2 x))/2 = ^?cos(x)^2 cos(x)^2 = a million/2 (a million+cos(2 x)): a million/2+(cos(2 x))/2 = ^?(a million+cos(2 x))/2 (a million+cos(2 x))/2 = a million/2+a million/2 cos(2 x): a million/2+(cos(2 x))/2 = ^?a million/2+(cos(2 x))/2 The left hand ingredient and correct hand ingredient are comparable: answer: | | (id has been validated)

Answer 4

[tan*cot] - cos^2
[sin/cos * cos/sin] - cos^2
1 - cos^2
= sin^2

Answer 5

tanx cotx - cos²x = sin²x

(sinx/cosx)(cosx/sinx) - cos²x = sin²x

1 - cos²x = sin²x

sin²x = sin²x
.