Question

cos(x)-sin(x)=sqrt(2)sin(x) prove that cos(x)+sin(x)=sqrt(2)cos(x)

Answer 1

are you still there?

Answer 2

@RahulYadav-2000

Answer 3

hey my internet connection is bad that's why it gets disconnected if any body knows the answer pls send it to me

Answer 4

If
\[cosx - sinx = \sqrt2 sinx\]
then
\[(1/\sqrt2) cosx - (1/\sqrt2) sinx = sinx\]
and
\[\cos \pi/4cosx - \sin \pi/4sinx = sinx\]
hence
\[\cos (x + \pi/4) = sinx\]
so
\[\sin(\pi/4 -x) = sinx\]
and this leads to
\[x=\pi/4\]

Answer 5

sorry it leads to
\[x=\pi/8\]

Answer 6

so in order to prove the second statement just substitute
\[x = \pi/8\] to both sides

Answer 7

1.f(x)= log(\[\sqrt{x ^{2}+1}\]-x)
2.f(x)= xlog(\[x+\sqrt{x ^{2} +1}\])
find which is odd and which is even