Question

prove cos(3pi/2 + x) = sin(x)

Answer 1

Since...it is a Odd multiple...Cos will Change to Sin and Since it is in Fourth Quadrant Cos is +ve

so cos(3pi/2 + x) = Sin x

Answer 2

cos 3 pi /2 = 0
sin 0 = 0
therefore
cos 3 pi/2 = sin 0
now add x to both sides
cos ( 3 pi/2 + x) = sin x

Answer 3

You can't add x to both sides like that

Answer 4

That's not a proof by the way

Answer 5

x is variable
if we add constants then why not variables

Answer 6

use the sum or difference formula this is trig

Answer 7

You cannot add x to both sides in the manner that you have @uzumakhi. Either way your steps don't really prove much.

Answer 8

can you tell me a proper derivation of this?
@Hero

Answer 9

Actually, upon further review, it looks like your steps might be more legit than previously thought.

Answer 10

Although when setting two things equal to zero, things get kinda tricky and fuzzy.

Answer 11

is it cos(3pi/2 + x) = cos 3pi/2cosx - sin3pi/2sinx?

Answer 12

if we see graphically then both cos 3pi/2 and sin 0 have same value
that's why i do this

Answer 13

I'm gonna have to check with an expert on this to see if those steps are valid for a proof.

Answer 14

This,,,May Help... http://assets.openstudy.com/updates/attachments/50113794e4b009397c68ec2f-parthkohli-1343305757650-unitcircle.gif

Answer 15

Okay, I have the reason why you cannot add x inside a function like that

Answer 16

to both sides

Answer 17

so tell me

Answer 18

\[(1)^2 = (-1)^2\] is true

However,

(1 + x)^2 \ne (-1 + x)^2\]

Answer 19

\[(1 + x)^2 \ne (-1 + x)^2\]

Answer 20

actually, wait

Answer 21

\[-1 \ne 1\] to begin with The expert pointed that out, but in this case \[\cos(3pi/2) = \sin(0)\] so you're still winning in this regard.

Answer 22

I think that

cos(3pi/2) + x = sin(0) + x is valid

but what you've done may not be

Answer 23

But it still isn't really clear why your step is truly invalid

Answer 24

but there is alternative derivation to prove this
which should be appropriate

Answer 25

Okay, here's a better and more convincing disproof of your methods

Answer 26

sin(0) = 0
tan(0) = 0

sin(0) = tan(0)

Add x to both sides
sin(x) = tan(x)

Answer 27

but there is also a case that sin and cos are mostly same