come up with an expression equivalent to 1-tan^4(x)

Question

anonymous · Answer

the answer would look similar to sec-sec or something like that.
All I know is that sec is in the answer

vishweshshrimali5 · Answer

See.. first start with using the identity:

$a^2 - b^2 = (a-b)(a+b)$

anonymous · Answer

so (1-tan^2)(1+tan^2) ???

vishweshshrimali5 · Answer

Great!!

vishweshshrimali5 · Answer

Now what is 1+ tan^2 ?

anonymous · Answer

sec^2x

vishweshshrimali5 · Answer

Good!

vishweshshrimali5 · Answer

Anything you can think about our second buddy... 1 - tan^2 x ?

anonymous · Answer

? would I have to separate that?

anonymous · Answer

(1-tanx)(1+tanx) ???

vishweshshrimali5 · Answer

I think just leave that 1-tan^2 x

anonymous · Answer

oh.

vishweshshrimali5 · Answer

You wanted a sec^2 right? You got that already :)

anonymous · Answer

I have it. but the answer choices have sec on both sides

anonymous · Answer

answer choices r faded so its hard to see

vishweshshrimali5 · Answer

Ohh well that's a tough task then...

anonymous · Answer

like one is 2sec^2x-sec^4x......or -2sec^2x-sec^4x

anonymous · Answer

thats 2 answer choices right there

vishweshshrimali5 · Answer

hmm... well let's see what we have till now...

$1-\tan^4 x$
$=(1-\tan^2 x)(\sec^2x)$

vishweshshrimali5 · Answer

There are several things we can do for 1 - tan^2

Like we have..

$$\cos(2x) = \frac{1- \tan^2 x}{1+\tan^2 x}$$

vishweshshrimali5 · Answer

So, if I replace 1- tan^2 x with cos(2x) (sec^2x)

anonymous · Answer

for example.... Which of the following expressions is equal to 1-sec^4x????
A. -2tan^2x-tan^4x           C. 2tan^2x-tan^4x
B. tan^2x-tan^4x               D. -2tan^2x+tan^4x

The answer was A..... So for the problem we were doing I thought it would be similar.

vishweshshrimali5 · Answer

I don't think there is any use of simplifying it any further... let's just go with cos(2x)*sec^4 x

anonymous · Answer

Same here, but its not any one of the answer choices.

anonymous · Answer

But I appreciate your help!

vishweshshrimali5 · Answer

Your welcome :)

faiqraees · Answer

So what are your choices?

faiqraees · Answer

Btw you can write 1-tan²x as 2 - sec²x

anonymous · Answer

Very hard to see as i did get a faded print out but from what I can manage to make out I have A.2sec^4x+sec^4x    B. sec^2x-sec^4x  C. 2sec^2x-sec^4x  D. -2sec^2x-sec^4x

faiqraees · Answer

yeah so C is correct

anonymous · Answer

so my answer would be positive?

faiqraees · Answer

(2-sec²x)sec²x
2sec²x-sec^4x

anonymous · Answer

ohhhh

anonymous · Answer

thanks a lot