Question

Verify: (sinx+cosx)^2=1+sin(2x)

Answer 1

(sinx+cosx)^2 = sin^2x + cos^2x + 2sinxcosx {formula for (a+b)^2}
= 1+ sin(2x) { since sin^2x + cos^2x = 1 }

Answer 2

If you want to verify (not to prove) substitute a value (for exampl pi/6) for LHS and RHS and see whether they are equal

Answer 3

\[\large {(\sin x+\cos x)^2=1+\sin2x}\]expand the parenthesis:\[(\sin x +\cos x)(\sin x+\cos x)=1+\sin x\]\[\color{red}{\sin^2x+2\sin x\cos x + \cos^2x}=1+\sin2x\]use the Pythagorean identity, \(\sin^2x+\cos^2x=1\)\[\color{red}{1}+2\sin x\cos x=1+\sin2x\]use the double-angle identity, \(1+2\sin x\cos x=1+\sin2x\):\[\color{red}{1+\sin2x}=1+\sin2x\]

Answer 4

hope that helps! @LindyLunt :)

Answer 5

My @yum is so colorful always.

Answer 6

-_- ..