Question

Simplify : Cos(x)Sec(x)-Cos^2(x)

Answer 1

First thing: by definition sec x = 1/cos x.

Hence cos x . sec x = 1.

Now it should be easy to see what to do.

Answer 2

so is the answer Sin^2(x)? or Cos^2(x)?

Answer 3

Cos(x)Sec(x)-Cos^2(x) = 1 - Cos^2(x)
and what does that equal?

Answer 4

Cot(x) = 1+Cos^2(x)? lol? im so confused now. where did that equation come from? this suppose to be simplified. Dont you change Sec(x) or Cos(x) in to sec or Cos? inorder to cross out each one and that will leave 1. Then 1 - Cos^2(x). What does 1-Cos^(x) equal to? is it Sin^2(x)???? or Cos^2(x)

Answer 5

it can't be case that 1 - cos^2 x = cos^2 x in general, because if it did, then
\[2 \cos^2 x = 1 \implies \cos^2 x = 1/2\]
in general and we know cos x varies.

But what we do know (or should know!) is that
\[\sin^2 x + \cos^2 x = 1\]
Hence
\[1 - \sin^2x = \cos^2 x\]
and
\[1 - \cos^2 x = \sin^2 x\]

(And yes of course cos x and sec x cancel each other because
\[\cos x . \sec x = \cos x \frac{1}{\cos x} =1\]
)

Answer 6

So do you see the the final answer now?