展開する sin(x)(1-sec(x))(1+x^2)

解

展開する

sin (x) (1 - sec (x)) (1 + x^{2})

x^{2} sin (x) - x^{2} tan (x) + sin (x) - tan (x)

解答ステップ

sin (x) (1 - sec (x)) (1 + x^{2})

拡張

sin (x) (1 - sec (x)) (1 + x^{2}) : sin (x) (1 + x^{2} - sec (x) - x^{2} sec (x))

= sin (x) (1 + x^{2} - sec (x) - x^{2} sec (x))

括弧を分配する

= sin (x) \cdot 1 + sin (x) x^{2} + sin (x) (- sec (x)) + sin (x) (- x^{2} sec (x))

簡素化

sin (x) \cdot 1 + sin (x) x^{2} + sin (x) (- sec (x)) + sin (x) (- x^{2} sec (x)) : x^{2} sin (x) - x^{2} tan (x) + sin (x) - tan (x)

= x^{2} sin (x) - x^{2} tan (x) + sin (x) - tan (x)