Question

Need help with Trigonometric Identies
cos^2x - sin^2x = 2cos^2x - 1
If someone could also explain the process it would be a big help

Answer 1

Oh this one easy!!
I am usually terribel at these

Answer 2

Let us start with the Left hand side

Answer 3

As we know Sin^2x+cos^2x=1

Answer 4

So let us say in our original equation Cos^2x-sin^2x we subsitute the -sin^2x with something else so it easier to solve

Answer 5

As we know from the identity that i showed you above
-sin^2x=Cos^2x-1
so we will plug this into -sin^2x in our original equation

Answer 6

cos^2x+(cos^2x-1)
2cos^2x-1

Answer 7

And we got the same answer as the right hand side

Answer 8

Did you get how i used the identity to sove it???
Cuz that was really not clear

Answer 9

Haha not exactly, it was a bit hard to follow

Answer 10

ok well i showed you that there is one identity Sin^2x+cos^2x=1
Do u know this?

Answer 11

Are u there?

Answer 12

Yes

Answer 13

So u got that?

Answer 14

Yup

Answer 15

ok now if I wld like i can rearrange this equation right?

Answer 16

cos^2x=-sin^2x+1

Answer 17

whtvr i can rearrange it which ever way i want as long as it equals the same

Answer 18

Yup
Cos^2x = 1 - Sin^2x
or
Sin^2x = 1 - Cos^2x

Answer 19

Yahoo!!!!

Answer 20

ok so I decide to reaarange it differently I bring the sin^2x to the right side and bring the one to the left side

Answer 21

Okay

Answer 22

cos^2x-1=-sin^2x

Answer 23

I just flipped some values over that is it

Answer 24

Okay

Answer 25

So then since -sin^2x equals cos^2x1 I can plug this into the original equation

Answer 26

cos^2x+(cos^2x-1)

Answer 27

I follow what you're doing, but I'm confused on how to write that

Answer 28

Well I just showed you how

Answer 29

Oh okay

Answer 30

Then open up the brackets and simplify and there is ur answer

Answer 31

Oh I see, thank you! Would you mind helping me on one more?
tanxcscxcosx = 1

Answer 32

let me see if i can figure this out. I am terrible at this!!!!

Answer 33

Oh this one i ssimple

Answer 34

Oh really? Cause I was trying to do the problem and it came out retarded