Question

If cosA - sinA = root 2 sinA, prove that cosA + sinA = root 2 cosA

Answer 1

any ideas??

Answer 2

Oh hello, Aayush bhai! :P Maybe, we could start off by squaring both the sides

Answer 3

Hello :))
And yeah that will be a great start

Answer 4

\[(cosA - sinA)^{2} = (\sqrt{2}sinA)^{2}\]

Answer 5

Thank you! ;-;

Answer 6

Try to square both equation and then add them
Aw np :)

Answer 7

I didn't get you there.. ;-;

Answer 8

If the second equation is true then
IF the RHS equals the LHS when you square and add the both the equation then we can say that second equation is true

Answer 9

Theres one more way to do this tho js

Answer 10

Easier?

Answer 11

Yeah the other method is a bit less confusing

Answer 12

Enlighten me, bro :P

Answer 13

Other method-
Step one: square both sides of the already given equation

Answer 14

I see

Answer 15

\[(cosA - sinA)^{2} = 2sinA\] ??

Answer 16

Then we could expand LHS?

Answer 17

Yeah expand the LHS
And it must be sin^2A on the right side tho

Answer 18

Oh yea, that's what I meant xD

Answer 19

xD okay expand the express

Answer 20

cos^2A + sin^2A - 2sinAcosA?

Answer 21

Expression*

Answer 22

Yeah right
Now sin^2A+cos^2A is 1

Answer 23

Right

Answer 24

Now we will move the 2sin^2A to the left and - 2sinAcosA to the right

Answer 25

So you'll get
1-2sin^A=2sinAcosA

oky??

Answer 26

Oh, u just exchange places.. right?

Answer 27

Yeah

Answer 28

Next we add 1 on both the sides

Answer 29

1+1-2sin^A=1+2sinAcosA
2(1-sin^2A)=sin^2A+ cos^2A +2sinAcosA

Answer 30

Oh

Answer 31

Then we change sin^2A + cos^A in RHS to 1?

Answer 32

Yeah the 1 on the RHS was changed into sin^2A+cos^2A

Answer 33

Soo are all those steps clear?

Answer 34

Yup!

Answer 35

Alright :D next we write that 1-sin^2A as cos^2A andd the RHS as (cosA+sinA) ^2

Answer 36

Oh

Answer 37

Okay what should we do next

Answer 38

Hmm

Answer 39

Idk

Answer 40

;-;

Answer 41

Okay you're confused somewhere
Tell me where

Answer 42

Now we have,
cos^2A = (cos+sin)^2, right?

Answer 43

Theres a 2 on the left

2(cos^2A) <-LHS

Answer 44

Oh

Answer 45

Yeah now we just gotta square root LHS and RHS

Answer 46

2cosA = cosA + sinA?

Answer 47

Then we could take cosA to the left, so cosA = sinA?

Answer 48

That will be root2cosA

Answer 49

So you have sinA+cosA=root2cosA

Answer 50

Oh yes, I'm soo careless

Answer 51

Aha, its proved then!

Answer 52

Yeah =]

Answer 53

Tysm! :D

Answer 54

Np :)