Question

help please.

find all solutions cos2x + 2 cos x + 1 = 0

Answer 1

cos^2** for the first part

Answer 2

This is a quadratic equation in cos(x).
If necessary you can make the substitution u = cos(x).
u^2 + 2u + 1 = 0
solve the quadratic, then put cos(x) back in place of u and solve for x.

Answer 3

how do i solve the quadratic

Answer 4

cos^2+cos=-1/2?

Answer 5

u^2 + 2u + 1 = 0
u^2 + u + u + 1 = 0
u(u+1) + 1(u+1) = 0
(u+1)(u+1) = 0
(u+1)^2 = 0
u+1 = 0
u = -1
put u = cos(x) back.
cos(x) = -1
solve for x.

Answer 6

so x=pi

Answer 7

\[\Large x = \pi \pm 2n \pi \]

Answer 8

thank you! do you mind explaining another problem/concept to me?

Answer 9

go ahead and post the question. I will try.

Answer 10

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

1.cot x sec4x = cot x + 2 tan x + tan3x

Answer 11

since , cos2x=2cos^2 x-1
2cos^2x -1 +2cosx +1=0
taking 2 cosx common and 1 is cancel from -1
2cosx(cosx+1)=0
either,
2cosx=0 or cosx+1 =0
cosx=0 or cosx=-1
\[[x=\cos^{-1} (0)] or [x=\cos^{-1} (-1)]\]
x=1 or x=cos^-1 (-1)
this is the answer

Answer 12

oh my .. lol can anyone help with that other question? ^^

Answer 13

@ashlean In the first problem you are sure the first term is cos^2(x) and NOT cos(2x) right? Because in the original problem posting you wrote cos(2x) and in the comment you changed it to cos^2(x) and @Haseeb96's solution above is for the original posting and not the correction in your first reply.

Answer 14

youre correct because idid chano cos^2 x

Answer 15

For the second problem, if you factor out cot(x) on the right, you get:
cot(x)(1 + 2tanx/cotx + tan3x/cotx)

Left side has cotx * sec(4x)

So we need to prove sec(4x) = (1 + 2tanx/cotx + tan3x/cotx)

I'd probably change everything into sine and cosine and substitute the appropriate identities and prove they are the same.

Answer 16

I think changing everything to tan(x) might work. sec(4x) = 1/cos(4x) = 1/cos(2*2x)
and cos(2A) = (1-tan^2(A))/(1+tan^2(A))
Put A = 2x and you will get everything in tan. You have to apply the double angle formula again to reduce everything to tan(x) and powers of tan(x) such as: tan^2(x), tan^3(x), tan^4(x), etc.

On the right: tan(3x) can be written as: (3tan(x) - tan^3(x))/(1-3tan^2(x))

Just a whole bunch of terms to deal with but if you have everything as tan(x) the left and right should simplify to the same thing.

I looked up some of the trig identities here (about half page down):
http://en.wikipedia.org/wiki/List_of_trigonometric_identities