Express as a single trigonometric function?

Question

cos^2 x - sin^2 x = ?

How can I simplify this, I am having problems with the square roots not sure what to do with them or how to approach! Thanks!

Answer 1

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cos^2 x - sin^2 x = 1

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Answer 2

You do not want to use square roots on this one!

It looks like you're learning the addition formulae for trig functions:

cos (A-B) = cos A cos B + sin A sin B
cos (A+B) = cos A cos B - sin A sin B
sin (A+B) = sin A cos B + cos A sin B
sin (A-B) = sin A cos B - cos A sin B

If you let A = B = x, one of these will do the trick.

Answer 3

cos^2 x - sin^2x = cos ^2 x - (1-cos ^2 x) = 2cos^2 x -1

Answer 4

short answer: csc theta - (cot theta)(cos theta) = sin theta long answer/information: i'm going to replace theta with x simply by fact this is extra straightforward to verify and form bear in mind that csc = a million/sin and cot=cos/sin csc x - (cot x)(cos x) = (a million/sin x) - (cos x/sin x)(cos x) = (a million/sin x) - (cos^2 x/sin x) =(a million-cos^2 x)/sin x = sin^2 x/sin x (formula: a million-cos^2 x = sin^2 x) =sin x observe that cos^2 x is "cos squared x, or (cos x) squared)

Answer 5

cos(x)^2 - sin(x)^2 = 1 - 2sin(x)^2 or 2cos(x)^2 - 1

ANS : cos(2x)

Info found at http://www.math.com/tables/trig/identities.htm

Answer 6

cos(2x) by double angle formula

Answer 7

1.

it's a pythagorean identity.