Simplify the expression? $cos(270+2alpha)+sin(450+2alpha)$

Question

Simplify:
$cos(270+2alpha)+sin(450+2alpha)$

AND if you know:
$3-4cos^2(3/2pi-alpha)$

There will be:

$3-4sin^2alpha$

OR

$3+4sin^2alpha$

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Answer 1 · 2017-04-09T15:24:54

I got $sin2alpha + cos2alpha$ .

I would use the following two formulas:

$cos(A + B) = cosAcosB - sinAsinB$
$sin(A + B) = sinAcosB + sinBcosA$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We have:

$cos(270)cos(2alpha) - sin(270)sin(2alpha) + sin(450)cos(2alpha) + cos(450)sin(2alpha)$

Because $5(90˚) = 450˚$ we have $sin450˚ = 1$ and $cos450˚ =0$ .

$-(-sin2alpha) + 1(cos2alpha) + 0(cos2alpha)$

$sin2alpha + cos2alpha$

I think this is as far as we can simplify.

Hopefully this helps!