Question

Verify each trigonometric equation help!

Answer 1

ok

Answer 2

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation
\[cotx \sec^4x = cotx +2 \tan x + \tan^3x\]x

Answer 3

I know this question is already posted on this website and answered, but it was being worked on the wrong side of the equal sign.

Answer 4

hmm ok ...

Answer 5

I need to figure out how to make the left side equal to the right, but I have a really hard time with proving identities for some reason

Answer 6

well this isn't a proof, you are just gonna use the identities to show that the equation is true,

Answer 7

oh, okay

Answer 8

1 sec

Answer 9

alright, thank you

Answer 10

i figured it out

Answer 11

awesome thanks! What would be my first step?

Answer 12

ill type it out, give me a sec

Answer 13

there may be a shorter way, but this works

Answer 14

first step is to write all the terms in just sin and cos powers, ...

Answer 15

\[\frac{ \cos x }{ \sin x }\frac{ 1 }{ \cos^4x } = \frac{ \cos x }{ \sin x } + \frac{ 2\sin x }{ \cos x } + \frac{ \sin^3 x }{ \cos^3 x }\]

Answer 16

ok write that down first on paper

Answer 17

we are then going to multiply both sides by the common denominator,
\[\frac{ \sin x \cos^4 x }{ \sin x \cos^4 x }\]

Answer 18

which gives you
\[\frac{ \cos x }{ \sin x \cos^4 x } = \frac{ \cos x \cos^4 x }{ \sin x \cos^4 x } + \frac{ 2 \sin^2 x \cos^3 x }{ \sin x \cos^4 x } + \frac{ \sin^4 x \cos x}{ \sin x \cos^4 x }\]

Answer 19

we are almost there...

Answer 20

i'm trying my hardest to follow haha..

Answer 21

since everything is divided by the same, you can multiply everything by the denominator to just equate the numerators

\[\cos x = \cos^5 x + 2\sin^2 x \cos^3 x + \sin^4 x \cos x\]

Answer 22

The right side can be written in the form (a + b)^2

\[1 = [ \sin^2 x + \cos^2 x]^2\]

Answer 23

and from the identities, you know sin^2(x) + cos^2(x) = 1

so

1 = 1^2

TRUE

Answer 24

That was a fun one, and there probably is a shorter way, but this also works as show.

Answer 25

haha well thank you for the explanation! But how did you go about rewriting cot and tan in cos and sin?

Answer 26

\[\cot(x) = \frac{ 1 }{ \tan(x) } = \frac{ 1 }{ \frac{ \sin(x) }{ \cos(x) } } = \frac{ \cos(x) }{ \sin(x) }\]

Answer 27

Tan(x) = sin(x) / cos(x)

Answer 28

@Jhannybean Hey check this one out, I showed it is true, but i probably missed a shortcut identity somewhere.

Answer 29

oh wow.. okay, easy enough! haha

Answer 30

any more fun ones like that?

Answer 31

\[\cos x = \cos^5 x + 2\sin^2 x \cos^3 x + \sin^4 x \cos x\]How did you get from this step to this one: \[1 = [ \sin^2 x + \cos^2 x]^2\]Did you just divide both siddes by \(\cos(x)\)?

Answer 32

yea, oh yeah i deleted that one because of a typo

Answer 33

Ok :)