Question

Which are identities?

Thanks you guys sooo much!

I think #1, #3, and #4 are identities.

Answer 1

Right-O!!

Answer 2

start with

sin^2(x) + cos^2(x) = 1 Call it equation A

tan(x) = sin(x)/cos(x)


for Question 1

tan(2x) = 2tan(x)/(1 - tan^2x)

take the reciporcal of each term

1/2tan(x) = (1-tan^2(x))/(2tan(x))

2. Expand the perfect square

(sin(x) -cos(x))(sin(x)-cos(x)) = sin^2(x) - 2sin(x)cos(x) + cos^2(x)
= 1 - 2sin(x)cos(x)

2sin(x)cos(x) =sin(2x) = 1 -sin(2x)


might be a typo in the question

3. \[\sin(8x) = \sin(2\times 4x) = 2\sin(4x)\cos(4x)\]


hope this helps