Which of the following is equivalent to 1 − cos 2 θ/cos 2 θ?
A. sec2 θ
B. (csc 2 θ ) -1
C. tan 2 θ
D. sin 2 θ
E. –1/sin2 θ
you must mean
(1 - cos^2 Ø) / cos^2 Ø
(the way you typed it, you would get 1-1 = 0 )
(1 - cos^2 Ø) / cos^2 Ø
= sin^2 Ø/cos^2 Ø
= tan^2 Ø
sorry, they're all squared θ not 2 θ
To solve this problem, let's simplify the expression and find an equivalent expression.
First, we can simplify 1 - cos^2θ by using the identity: 1 - cos^2θ = sin^2θ.
Therefore, the expression becomes sin^2θ / cos^2θ.
Next, let's simplify this expression further. We know that sin^2θ / cos^2θ is equivalent to (sinθ / cosθ)^2, which is the square of the tangent function, tan^2θ.
Therefore, the correct answer is option C: tan 2θ.
To arrive at this conclusion, we used the trigonometric identity sin^2θ / cos^2θ = tan^2θ. It is important to be familiar with trigonometric identities and how to manipulate them in order to solve such problems.