展開する 1/12 (sin(x^2)+cos(x^2))(4+sin(2)x^2)

解

展開する

\frac{1}{12} (sin (x^{2}) + cos (x^{2})) (4 + sin (2) x^{2})

\frac{sin ( x ^{2} ) + cos ( x ^{2} )}{3} + \frac{x ^{2} sin ( x ^{2} ) sin ( 2 ) + x ^{2} cos ( x ^{2} ) sin ( 2 )}{12}

解答ステップ

\frac{1}{12} (sin (x^{2}) + cos (x^{2})) (4 + sin (2) x^{2})

拡張

\frac{1}{12} (sin (x^{2}) + cos (x^{2})) (4 + sin (2) x^{2}) : \frac{1}{12} (4 sin (x^{2}) + x^{2} sin (x^{2}) sin (2) + 4 cos (x^{2}) + x^{2} cos (x^{2}) sin (2))

= \frac{1}{12} (4 sin (x^{2}) + x^{2} sin (x^{2}) sin (2) + 4 cos (x^{2}) + x^{2} cos (x^{2}) sin (2))

括弧を分配する

= \frac{1}{12} \cdot 4 sin (x^{2}) + \frac{1}{12} x^{2} sin (x^{2}) sin (2) + \frac{1}{12} \cdot 4 cos (x^{2}) + \frac{1}{12} x^{2} cos (x^{2}) sin (2)

簡素化

\frac{1}{12} \cdot 4 sin (x^{2}) + \frac{1}{12} x^{2} sin (x^{2}) sin (2) + \frac{1}{12} \cdot 4 cos (x^{2}) + \frac{1}{12} x^{2} cos (x^{2}) sin (2) : \frac{sin ( x ^{2} ) + cos ( x ^{2} )}{3} + \frac{x ^{2} sin ( x ^{2} ) sin ( 2 ) + x ^{2} cos ( x ^{2} ) sin ( 2 )}{12}

= \frac{sin ( x ^{2} ) + cos ( x ^{2} )}{3} + \frac{x ^{2} sin ( x ^{2} ) sin ( 2 ) + x ^{2} cos ( x ^{2} ) sin ( 2 )}{12}