Question

How do I prove this identity?
(sin x +cos x)2 = 1 + 2 sin x cos x

Answer 1

i suppose that \[\large \rm (\sin x+\cos x )^2=1+2\sin x \cos x\]

Answer 2

just expand the left hand side

Answer 3

I don't know how to expand it

Answer 4

\[\large (\sin x+ \cos x)^2=(\sin x +\cos x)(\sin x+\cos x)\]

Answer 5

well if you don't know that is a big problem

Answer 6

do you know how to expand this binomial
\[(a+b)^2\]

Answer 7

I was in the hospital for a month so this is a pain to catch up on and no

Answer 8

even if you are in hospital does not mean you have and excuse my dear
expanding a binomial is something your learn from basic algebra not even this

Answer 9

binomial expansion for (a+b)^2 is
\[\large \rm (a+b)^2=(a+b)(a+b)=a^2+ab+b^2\]

Answer 10

now use the same method to expand
\[\large \rm (\sin x+\cos x)^2\]

Answer 11

let sinx = s and cos x = c
(s + c)^2 = s^2 + c^2 + 2 sc
but s^2 + c^2 = 1

so right side = 1 + 2sc
1 + 2sin x cos x

Answer 12

you shouldn't give answer that @welshfella
the poster needs to work the rest himself/herself to learn

Answer 13

yes ur right