# Thread: Need steps how to solve this little problem!

1. ## Need steps how to solve this little problem!

(Trigonometric Functions and Identities)

1. Which of the following is equivalent to ?

A. sec2
B. (csc2) - 1
C. tan2
D. sin2
E.

I need to know how they managed to get to C as an answer. Help Please...

2. One way of going to it is to see that:

$\displaystyle \frac {1 - \cos^2 \theta} {\cos^2 \theta} = \frac {1} {\cos^2 \theta} - \frac {\cos^2 \theta} {\cos^2 \theta} = \sec^2 \theta - 1 = \tan^2 \theta$

... are you sure you copied the Q down right?

3. Thank you soo much.

I am studying for a Compass Math Placement test tomorrow. here is where I got question.
ACT's COMPASS System: Sample Questions for Trigonometry

I forgot that the 1 also has the Cos value under it. Thanks for the help.

4. Another one !

Use identity $\displaystyle \sin^2 \theta+\cos^2 \theta=1 \implies 1-\cos^2 \theta=\sin^2 \theta$

So $\displaystyle \frac{1-\cos^2 \theta}{\cos^2 \theta}=\frac{\sin^2 \theta}{\cos^2 \theta}=\tan^2 \theta$