Use the binomial expansion to find the real and imaginary parts of $(cosθ+isinθ)^5$ Hence show that $sin5θ/sinθ=16cos^4θ-12cos^2θ+1$
I expanded this expression and I got: $cos^5θ+5icos^4θsinθ-10cos^3θsin^2θ-10icos^2θsin^3θ+5cosθsin^4θ+isin^5θ$
Then I used the Moivre's theorem and I got: $(cos5θ+isin5θ)$
I compared the imaginary parts and I got something like: $sin5θ=5cos^4θsinθ-10cos^2θsin^3θ+sin^5θ$
which is very close to: $(16cos^4θ-12cos^2θ+1)sinθ$ but not the same.
Where do I make te mistake?
Thanks for any help! ;)