Question

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

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

Answer 1

i am completely lost

Answer 2

\[cot x sec^4 x = cot x +2tan x +tan^3x\\or~ cotx sec (4x)= cotx +2 tan x + tan (3x)\]

Answer 3

first one

Answer 4

just sec^4 = (1+tan^2)^2 and open it, then time cot into the expanding, and.... got the RHS

Answer 5

what?

Answer 6

Yeah, once you make it into (1+tan^2(x))^2, you'll be switching your cot and your tan into sines and cosines to solve from there.

Answer 7

@nickolgee429 have you covered yet binomial theorem?

Answer 8

is that just separating the binomial into two parts? @jdoe0001

Answer 9

into 3 parts

Answer 10

a perfect square \(\bf \text{trinomial}\)

Answer 11

@Psymon no need to turn to sin/cos

Answer 12

but its to the power of 2? so wouldn't i make (1+tan^2(x))^2 into (1+tan^2(x))x(1+tan^2(x))

Answer 13

Probably not, but it makes it visually easier to see if you're not used to it. I'm obviously no expert at it, but it lets me know for sure what I'm doing. It's a safe bet for me personally.

Answer 14

@nickolgee429 yes it does, as @Loser66 correctly pointed out, expand that, and then multiply by cot(x)

Answer 15

hmmm one sec.... it doesn't expand in to THAT

Answer 16

ok, let me show my work.

Answer 17

@nickolgee429 I'm assuming you know what a perfect square trinomial is?

Answer 18

like this: cot (x) times (1+tan^2(x)) times(1+tan^2(x))? and yes i know what a perfect square trinomial is.

Answer 19

\[cot (1 + tan^2)^2= cot (1 + 2 tan^2 + tan^4) = cot +\frac {2tan^2}{tan}+ \frac {tan^4}{tan}\]
cot +2 tan+ tan^3

Answer 20

hmmm http://statisticslectures.com/images/trinomial11.gif

Answer 21

because cot = \(\dfrac {1}{tan}\)

Answer 22

ohh cot = \[\frac{ 1 }{ \tan }\]

Answer 23

ok now i get it! Thanks everyone!

Answer 24

yw