Simplifying Trig Ratio Identities: Does This Answer Make Sense?

[supernova1203]

Trig ratios identities problems, in this case i am not asked to prove anything, just asked to simplify(Solve)

im left with

(1/costheta)(1/costheta)

At this point do we cross multiply?

we would end up with

costheta/costheta = 1

does this make sense? I encountered a similar problem earlier and it was somewhat like this where the solution was 1.

 

[niklaus]

are you saying that from

x = (1/cos(theta))(1/cos(theta))

you arrive at cos(theta)/cos(theta) = x = 1?

that would not be correct...

however the statement

cos(theta)/cos(theta) = 1 would certainly be correct

 

[mharten1]

No, it isn't correct.

You do not cross multiply unless they are equal to each other. In this case, you should multiply normally. You started with (1/cosθ)(1/cosθ), correct?

So in that case (1/cosθ)(1/cosθ) = 1/cos²θ = sec²θ

 

[Calrid]

Yes it doesn't add up

For example 1/cos(theta) x 1/cos (theta) is the same as saying 1/cos^2(theta) does this equal 1?

Find a trig identity that would explain it in different terms I think is your best bet.

Ok that was redundant whs^.

 

[HallsofIvy]

$$\frac{1}{a}\frac{1}{a}= \frac{1}{a^2}$$
not 1.

If you were dividing, it would be
$$\frac{\frac{1}{a}}{\frac{1}{a}}= 1$$