Question

Which of the following are identities? (and why)

(sinx-cosx)^2=1+sin2x

1-tan^2x/2tanx=1/tan2x

sin x + sin5x/cosx+cos5x=tan3x

Answer 1

(sinx - cosx)^2 = (sin x - cos x)(sin x - cos x)
= sin^2(x) - 2sin x cos x + cos^2(x)

does this expression equal 1 +sin^(2)x?

Answer 2

no

Answer 3

yeah, it doesn't. sin^2(x) + cos^2(x) = 1, so it equals 1 - 2sin(x)cos(x), not 1 + sin^2(x)

Answer 4

so there's one

Answer 5

are either of the other two identities though? how would you begin to solve either of them?

Answer 6

You expand them into different expressions and check their equivalence