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Popular >

simplify [cos(2t-pi/3)]^2

Solution

simplify

[cos (2 t - \frac{π}{3})]^{2}

Solution

\frac{1}{4} cos^{2} (2 t) + \frac{3}{2} cos (2 t) sin (2 t) + \frac{3}{4} sin^{2} (2 t)

Solution steps

cos^{2} (2 t - \frac{π}{3})

Rewrite using trig identities

= (\frac{1}{2} cos (2 t) + \frac{3}{2} sin (2 t))^{2}

Simplify

(\frac{1}{2} cos (2 t) + \frac{3}{2} sin (2 t))^{2} : \frac{1}{4} cos^{2} (2 t) + \frac{3}{2} cos (2 t) sin (2 t) + \frac{3}{4} sin^{2} (2 t)

= \frac{1}{4} cos^{2} (2 t) + \frac{3}{2} cos (2 t) sin (2 t) + \frac{3}{4} sin^{2} (2 t)

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Frequently Asked Questions (FAQ)

What is [cos(2t-pi/3)]^2 ?
The solution to [cos(2t-pi/3)]^2 is 1/4 cos^2(2t)+(sqrt(3))/2 cos(2t)sin(2t)+3/4 sin^2(2t)