Question

How do you get from sqrt((4sin^(2)2t)+(16cos^(2)2t)) to sqrt(1+3cos^(2)2t)?

Answer 1

\[\sqrt{4 \sin^2 (2t) + 16 \cos^2 (2t)}\]\[= \sqrt{4\sin^2 (2t) + 4 \cos^2 (2t) + 12 \cos^2(2t)}\]\[= \sqrt{4 + 12 \cos^2 (2t)}\]\[= 2\sqrt{1 + 3\cos^2(2t)}\]

Answer 2

well I would have said to start split cos

\[\sqrt{4\sin^2(2t) + 4\cos^2(2t) + 12\cos^2(2t)}\]

which becomes

\[\sqrt{4(\sin^2(2t) + \cos^2(2t)) + 12 \cos^2(2t)}\]

now sin^2 + cos^2 = 1 so it becomes

\[\sqrt{4 + 12 \cos^2(2t)}\]

factor it and its

\[\sqrt{4(1 + 3 \cos^2(2t)}\]

can you simplify from here...?

Answer 3

Thank you guys!

Answer 4

No problem :)