Question

proof?
sinx+cosx=√2 sin(x+pi/4)

Answer 1

sum formula
sin(a+b) = sina cosb + sinb cosa

sin(x+pi/4) = cos(pi/4)sinx + sin(pi/4)cosx
cos(pi/4) = sin(pi/4) = sqrt2/2

sin(x+pi/4) = sqrt2/2 (sinx +cosx)
multiply by sqrt 2 and there you go

Answer 2

You see it right?

Answer 3

dumbcows derivation seems good.

Answer 4

\[\sqrt{2}\cos(x-\pi/4)=\sqrt{2}(cosx.\cos \pi/4 + sinx.\sin \pi/4)
=cosx+sinx\]
hey! \[\cos \pi/4=\cos \sqrt{2}/2 \sin \pi/4=si \sqrt{2}/2\]

Answer 5

Please note, it is useful to remember the general identity \[ \large \cos x \pm \sin x = \sqrt2 \sin(\frac{\pi}{4} \pm x) = \sqrt2 \cos( \frac{\pi}{4} \mp x) \]

Answer 6

foolformath, never had to learn that identity

Answer 7

This right?

Answer 8

@dumbdow Useful in competitive mathematics. (saves precious seconds during a contest)

Answer 9

With this software(Matlab) can I solve it?

Answer 10

solve what?

Answer 11

solve means proof

Answer 12

Hey, did you prove it?

Answer 13

i don't know if matlab will prove trig identities ?

Answer 14

Did you use it?

Answer 15

best way... divide and multiply by \[\sqrt{2}\] ...it becomes \[\sqrt{2}(1/\sqrt{2}sinx+ 1/\sqrt{2}cosx)\]

= \[\sqrt{2}\](sin ( pie/4 +x)

Answer 16

Akshat did you prove it?

Answer 17

if equation is like asinx + bcosx
then divide and multiply by \[\sqrt{a^2 + b^2}\] ...then convert it to the basic form of sin(x+\[\alpha\]

Answer 18

i showed the steps to prove equality in 1st post

Answer 19

Slim's dumbcow

Answer 20

dumbcow! I'm From Iran and I don't type english

Answer 21

Who did it prove?

Answer 22

oh ok , i'll redo it in easier form
\[\sqrt{2}\sin(x+\pi/4) = \sin x + \cos x\]
\[\sqrt{2}(\sqrt{2}/2\sin x + \sqrt{2}/2\cos x) = \sin x + \cos x\]
\[\sqrt{2}*\sqrt{2}/2(\sin x +\cos x) = \sin x +\cos x\]
\[\sin x + \cos x = \sin x +\cos x\]

Answer 23

Oh thank you!
I have a surprise for you(dumbcow)?

Answer 24

I'll send you a file now

Answer 25

Download It Now

Answer 26

umm what is it...if want to share something just attach it to this post

Answer 27

I wrote some of the photos is Persian