Question

1-2cos^2x/1-2cosx sinx= sinx+cosx/sinx-cosx

Answer 1

yes

Answer 2

we have used \(\sin^2x+\cos^2x=1\) , so many times!
but this is the type of problem when we use
\(\Large 1 = \sin^2x=\cos^2x\)

Answer 3

i mean \(\Large 1= \sin^2x+\cos^2x\)

Answer 4

so, take left side and substitute this for 1
what u get ?

Answer 5

sin^2x+cos^2x-2cos^2x/sin^2x+cos^2x-2cosxsinx

Answer 6

simplify the numerator
and notice that denominator is of the form a^2+b^2-2ab
what does that equal ?

Answer 7

I don't know, type the answer

Answer 8

oh, really ?
sorry, this is not an answering site! its a learning site :)

and try the numerator part , its easy!

Answer 9

ok sinx + cosx - 2cos^2x

Answer 10

How do I simplify

Answer 11

the num is actually
sin^2x+cos^2x-2cos^2x
right ?
whats
cos^2x-2cos^2x =.....?

factor out cos^2 x

Answer 12

Can you cross out the cos^2x and be left with sin^2x -2

Answer 13

not actually,
when we factor out,
cos^2x-2cos^2x = cos^2x (1-2) = - cos^2 x
got this ?

Answer 14

ok is the numerator sin^2x + sin^2x. I factored out a cos^2x, then I had 1-cos^2x, which is sin^2x

Answer 15

we were talking about num. only, which came out to be
sin^2x -cos^2x
isn't it ?

Answer 16

sin^2x + cos^2x-2cos^2x =sin^2x + cos^2x (1-2) = sin^2 x- cos^2 x
like this.

Answer 17

I don't know im so lost right now

Answer 18

look over the steps i gave you and ask in which step you have doubt

Answer 19

ok where does the (1-2) come from? How did you get that

Answer 20

you know factoring ?
like ab+ac = a(b+c) <<<<<[factoring out a]

so, cos^2x-2cos^2x = cos^2x (1-2) <<<<[factoring out cos^2x]

Answer 21

Can it be written as 1-cos^2x though

Answer 22

nopes, we need to factor OUT cos^2x from BOTh therms

Answer 23

Oh ok now I see it

Answer 24

I got that part

Answer 25

then what?

Answer 26

now a^2-b^2 = (a+b)(a-b)
so, what about cos^2x-sin^2x = .... ?

Answer 27

(cosx +sinx)(cosx-sinx)

Answer 28

But its sin^2x + cos^2x, not -

Answer 29

it is -
sin^2x + cos^2x-2cos^2x =sin^2x + cos^2x (1-2) = sin^2 x- cos^2 x
like this.

Answer 30

So you multiplied (1-2) through that

Answer 31

duh (1-2) is -1, then you times by a negative, which change the sign

Answer 32

yes, thats correct. glad you understood by yourself.

Answer 33

now the denominator

Answer 34

the denom is of the form a^2+b^2-2ab
which is = (a-b)^2

Answer 35

which would be (sinx - cosx)^2

Answer 36

absolutely correct!
and what gets cancelled out from numerator and denominator ?

Answer 37

The whole thing, top and bottom are both the same

Answer 38

not actually

Answer 39

No wait, (sinx - cos)^2 = (sinx-cos) (sinx-cosx), right?

Answer 40

correct!

Answer 41

what gets cancelled ? and what remains ?

Answer 42

sinx + cosx over sinx - cosx, which equals the right side

Answer 43

Omg your genius, thank you very much

Answer 44

you are welcome ^_^