Question

verify:
(sinx+cosx)squared=1+sin(2x)

Answer 1

Use foil first. on
\[\large (\sin x + \cos x)^2\]

Answer 2

can you show me how to solve it from the right side?

Answer 3

Sure. First, how do you perform the FOIL method, in squaring a binomial?

Answer 4

(x+y)² = x² + 2xy + y²
right?

Answer 5

yes, i got sin\[2^\]+cos\[2^\]+cos(x)sin(x)+sin(x)cos(x)

Answer 6

Or,
sin²x + cos²x + 2sinxcosx

Answer 7

according to the pathagorean identity you can combine the sine and cosine Squared to equal 1

Answer 8

so how do you get rid of the cosx?

Answer 9

Yeah, so you have
1 + 2sinxcosx

Now, what's the formula for
sin(a+b)
?

Answer 10

sinxcosy+cosxsiny

Answer 11

That's right :)
Now what's the formula for
sin(2x) = sin(x+x)
?

Answer 12

thank you, I forgot about that identity

Answer 13

So you can do it from here?

Answer 14

yeah, thanks

Answer 15

No problem.