Graph the expression sec^ 2 x - sec^ 2 x sin^ 2 x on your calculator. Determine what constant or single function is equivalent to the given expression

Question

anonymous · Answer

Factor out the $\sec^2x$.

anonymous · Answer

I did I got sin ^2x as whats left

psymon · Answer

Not quite :P

anonymous · Answer

$$\sec^2x-\sec^2x\sin^2x=\sec^2x\left(1-\sin^2x \right)$$

anonymous · Answer

Ok so it would be$$\sec ^2x - \sin^2x$$

psymon · Answer

Siths just wrote the answer you should have :P Might as well copy it, it is correct.

psymon · Answer

$$\sec ^{2}x(1-\sin ^{2}x)$$
If you multiplied it back in you would get the same answer you started with :3

anonymous · Answer

Ohhhhhhhh ok thanks guys can you help me on the ones I posted above this one I swear it will be the last one

psymon · Answer

Whoa, whoa, we're not done.

anonymous · Answer

Oh what

psymon · Answer

You can simplify what ya got there more. Use the fact that:
$$\sin ^{2}x+\cos ^{2}x=1$$ to rewrite that 1-sin^2(x) part.

anonymous · Answer

So would this be left $$\sec ^2x \times \cos^2x$$

psymon · Answer

Correct. Now what's the one last thing you can do to simplify that? :P

anonymous · Answer

$$\frac{ 1 }{ \cos^2x } \times \cos^2x $$

psymon · Answer

There ya go. Therefore:
$$f(x)=1$$

psymon · Answer

So all that mumbo jumbo was just a funky way of writing the line y = 1, lol.

anonymous · Answer

Yeah finally  can you help me with my last problem with explanations

psymon · Answer

What is it?

anonymous · Answer

I will post it as a new question hold on

psymon · Answer

kk