What is 1/2 sin(2t)(7/8 cos(4t)+3(t+1/4 sin(4t))) ?

The solution to 1/2 sin(2t)(7/8 cos(4t)+3(t+1/4 sin(4t))) is (sin(2t)(24t+7cos(4t)+6sin(4t)))/(16)

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simplify 1/2 sin(2t)(7/8 cos(4t)+3(t+1/4 sin(4t)))

simplify

\frac{1}{2} sin (2 t) (\frac{7}{8} cos (4 t) + 3 (t + \frac{1}{4} sin (4 t)))

\frac{sin ( 2 t ) ( 24 t + 7 cos ( 4 t ) + 6 sin ( 4 t ) )}{16}

Solution steps

\frac{1}{2} sin (2 t) (\frac{7}{8} cos (4 t) + 3 (t + \frac{1}{4} sin (4 t)))

Simplify

\frac{7}{8} cos (4 t) + 3 (t + \frac{1}{4} sin (4 t)) : \frac{7 cos ( 4 t )}{8} + 3 t + \frac{3 sin ( 4 t )}{4}

= \frac{1}{2} sin (2 t) (\frac{7 cos ( 4 t )}{8} + 3 t + \frac{3 sin ( 4 t )}{4})

Apply the fraction rule:

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

= \frac{1 \cdot sin ( 2 t ) ( \frac{7 c o s ( 4 t )}{8} + 3 t + \frac{3 s i n ( 4 t )}{4} )}{2}

Simplify

1 \cdot sin (2 t) (\frac{7 cos ( 4 t )}{8} + 3 t + \frac{3 sin ( 4 t )}{4}) : \frac{sin ( 2 t ) ( 24 t + 7 cos ( 4 t ) + 6 sin ( 4 t ) )}{8}

= \frac{\frac{s i n ( 2 t ) ( 24 t + 7 c o s ( 4 t ) + 6 s i n ( 4 t ) )}{8}}{2}

Apply the fraction rule:

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

= \frac{sin ( 2 t ) ( 24 t + 7 cos ( 4 t ) + 6 sin ( 4 t ) )}{8 \cdot 2}

Multiply the numbers:

8 \cdot 2 = 16

= \frac{sin ( 2 t ) ( 24 t + 7 cos ( 4 t ) + 6 sin ( 4 t ) )}{16}

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What is 1/2 sin(2t)(7/8 cos(4t)+3(t+1/4 sin(4t))) ?
The solution to 1/2 sin(2t)(7/8 cos(4t)+3(t+1/4 sin(4t))) is (sin(2t)(24t+7cos(4t)+6sin(4t)))/(16)