What is 1/2 (-1/6 csc^6(2x)+1/4 csc^4(2x)) ?

The solution to 1/2 (-1/6 csc^6(2x)+1/4 csc^4(2x)) is (-1/6 csc^6(2x)+1/4 csc^4(2x))/2

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simplify 1/2 (-1/6 csc^6(2x)+1/4 csc^4(2x))

simplify

\frac{1}{2} (- \frac{1}{6} csc^{6} (2 x) + \frac{1}{4} csc^{4} (2 x))

\frac{- \frac{1}{6} csc ^{6} ( 2 x ) + \frac{1}{4} csc ^{4} ( 2 x )}{2}

Solution steps

\frac{1}{2} (- \frac{1}{6} csc^{6} (2 x) + \frac{1}{4} csc^{4} (2 x))

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot ( - \frac{1}{6} csc ^{6} ( 2 x ) + \frac{1}{4} csc ^{4} ( 2 x ) )}{2}

Apply rule:

1 \cdot a = a

1 \cdot (- \frac{1}{6} csc^{6} (2 x) + \frac{1}{4} csc^{4} (2 x)) = (- \frac{1}{6} csc^{6} (2 x) + \frac{1}{4} csc^{4} (2 x))

= \frac{- \frac{1}{6} csc ^{6} ( 2 x ) + \frac{1}{4} csc ^{4} ( 2 x )}{2}

\frac{( w - 1 ) ^{2}}{2} + 4 - 2 w

\frac{x ( - x + 3 )}{2}

(t am x + cot (x)) cos (2 x)

- B (x^{2} - x + 1)^{2}

\frac{1}{2} (\frac{1}{2} sin (2 x) - \frac{1}{4} sin (4 x)) + C

What is 1/2 (-1/6 csc^6(2x)+1/4 csc^4(2x)) ?
The solution to 1/2 (-1/6 csc^6(2x)+1/4 csc^4(2x)) is (-1/6 csc^6(2x)+1/4 csc^4(2x))/2