Question

Verify that each equation is an identity.
1 + sin 2x = (sinx + cosx)^2

Answer 1

Start off with your left hand side.
So we have :
LHS = 1 + sin2x
(Now use the fact that sin2x = 2 sinx cosx)
= 1 + 2sinxcosx
(Now use the fact that sin^2x + cos^2x = 1)
= sin^2x + cos^2x + 2sinxcosx
(Re-arrange the equation and we get this:)
= sin^2x + 2sinxcosx + cos^2x

From this step ... you need to recall this basic quadratic rule thing LOL

a^2 + 2ab + b^2 = (a + b)^2
In your case, the a= sinx and b =cosx

Soooo,
= (sinx + cosx)^2
=RHS

tadaa

Answer 2

Thank you >o<

Answer 3

I think expanding the right hand side woulda been wayyy easier :3 but maybe that's just me hehe

Answer 4

My teacher told me specifically to do the left hand side for some reason. ^^'

Answer 5

When verifying, you're only allowed to mess with `one side`.
Doesn't usually matter which side you choose to fiddle with though.
Teacher wanted left side though huh? >.< Oh boyyy

Answer 6

you're welcome @uselesscookies
xD I think usually we use the left side but ON occasion we use the right side :)