Trigonometry + Algebra?
2007-09-30 06:58:16 · 4 answers · asked by Jupiter 1 in Science & Mathematics ➔ Mathematics
YES!!!!
(cosx + sinx)(cosx - sinx) =
cos^2x + sinxcosx - sinxcosx - sin^2x =
cos^2x - sin^2x =
cosxcosx - sinxsinx =
cos2x (a trig.identity).
2007-09-30 07:04:57 · answer #1 · answered by lenpol7 7 · 0⤊ 0⤋
Yes, it's true.
(cos x + sin x)(cos x - sin x) = cos^2 x - sin^2 x
cos 2x = 2.cos^2 x - 1 = 2.cos^2 x - (cos^2 x + sin^2 x) = cos^2 x - sin^2 x.
2007-09-30 14:07:11 · answer #2 · answered by Anonymous · 0⤊ 0⤋
let cos x = a
sin x = b
We know that (a+b)(a-b) = a^2 - b^2
=> (cos x + sin x)(cos x - sin x) = cox^2 (x) - sin^2 (x)
= cos^2 (x) - 1 + cox^2 (x)
= 2cos^2 (x) - 1
= cos 2x (proven)
line 2: recall that sin^2 (x) + cos^2 (x) = 1
so that sin^2 (x) = 1 - cos^2 (x)
2007-09-30 14:06:10 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Yes, it is true.
(cos x + sin x)(cos x - sin x)
(cosx)^2 - (sinx)^2 = cos2x
2007-09-30 14:07:46 · answer #4 · answered by Christine P 5 · 0⤊ 0⤋