## anonymous one year ago cos(x)-sin(x)=sqrt(2)sin(x) prove that cos(x)+sin(x)=sqrt(2)cos(x)

1. alekos

are you still there?

2. alekos

3. anonymous

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

4. alekos

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 $x=\pi/4$

5. alekos

sorry it leads to $x=\pi/8$

6. alekos

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

7. anonymous

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