Question

*Trigonometric Identities*

Answer 1

cos2 y − sin2 y = 1 − 2sin2 y

Answer 2

its cos^2y - sin^2y= 1 - 2sin^2y

Answer 3

try using the identity
sin^2 y + cos^2 y = 1

Answer 4

so change cos^2?

Answer 5

sin^y = 1 - cos^2y

Answer 6

isnt it better to change cos so ill have all sin?

Answer 7

replace cos^2 y by 1 - sin^2 y on the left side

Answer 8

so its
(1 - sin^2y) - sin^2y = 1- 2sin^2y

Answer 9

yes

Answer 10

1- 2sin^2y = 1-2siny

Answer 11

easy one this

Answer 12

huh?

Answer 13

- your last post was incorrect
the previous one completed the proof

Answer 14

but shouldnt both sides be the same thing?o.O

Answer 15

No
you have taken the left side and by using known trig identity converted it to the right side

Answer 16

- therefore the identity is true

Answer 17

1 - sin^2y) - sin^2y = 1- 2sin^2y

Answer 18

from here I expanded the brackets and got
1 - sin^2y - sin^2y = 1- 2sin^2y

Answer 19

- sin^2y - sin^2y = - 2 sin^2y

Answer 20

right??

Answer 21

cos^2y - sin^2y = 1 - 2sin^2y

now cos^2 y = 1 - sin^2 y so substituting

1 - sin^2 y - sin^2 y = 1 - 2 sin^2 y = RHS

Answer 22

yes

Answer 23

RHS = right hand side

Answer 24

so then wouldnt it be
1 - 2sin^2y = 1 - 2sin^2y??

Answer 25

no - no need to write that

usually with these , you pick the more complicated side of the identity and try to convert it to the other side . Once that is done you have confirmed the identity.

Answer 26

so wat will the answer be then? o.O

Answer 27

just write what i have put
or if you like at the end write
'the above proves the original identity'.

Answer 28

- thats what this is - a Proof.

Answer 29

so this is the answer?
1 - sin^2 y - sin^2 y = 1 - 2 sin^2 y = RHS

Answer 30

No there are 2 lines before that

- check 6 posts back.

Answer 31

the answer is the whole process of proving the identity

Answer 32

cos^2y - sin^2y = 1 - 2sin^2y

now cos^2 y = 1 - sin^2 y so substituting

1 - sin^2 y - sin^2 y = 1 - 2 sin^2 y = RHS

The above proves the original identity

Answer 33

you could also make a note to clarify that RHS = right hand side

Answer 34

gotta go - hope this has clarified things