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Popular >

expand sqrt(1+((2sin(2t))+(4cos(2t)))^2)

Solution

expand

1 + ((2 sin (2 t)) + (4 cos (2 t)))^{2}

Solution

1 + 4 sin^{2} (2 t) + 8 sin (4 t) + 16 cos^{2} (2 t)

Solution steps

1 + ((2 sin (2 t)) + (4 cos (2 t)))^{2}

Remove parentheses:

(a) = a

= 1 + (2 sin (2 t) + 4 cos (2 t))^{2}

Expand

1 + (2 sin (2 t) + 4 cos (2 t))^{2} : 1 + 4 sin^{2} (2 t) + 16 sin (2 t) cos (2 t) + 16 cos^{2} (2 t)

= 1 + 4 sin^{2} (2 t) + 16 sin (2 t) cos (2 t) + 16 cos^{2} (2 t)

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

sin (x) cos (x) = \frac{sin ( 2 x )}{2}

= 16 \cdot \frac{sin ( 2 \cdot 2 t )}{2}

Simplify

16 \cdot \frac{sin ( 2 \cdot 2 t )}{2} : 8 sin (4 t)

= 1 + 4 sin^{2} (2 t) + 8 sin (4 t) + 16 cos^{2} (2 t)

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Frequently Asked Questions (FAQ)

What is expand sqrt(1+((2sin(2t))+(4cos(2t)))^2) ?
The solution to expand sqrt(1+((2sin(2t))+(4cos(2t)))^2) is sqrt(1+4sin^2(2t)+8sin(4t)+16cos^2(2t))