展開する sin(x)cos(x)(tan(x)+csc(x))

解

展開する

sin (x) cos (x) (tan (x) + csc (x))

cot (x) sin (x) + sin^{2} (x)

解答ステップ

sin (x) cos (x) (tan (x) + csc (x))

= cos (x) sin (x) (tan (x) + csc (x))

分配法則を適用する:

a (b + c) = ab + a c

cos (x) sin (x) (tan (x) + csc (x)) = cos (x) sin (x) tan (x) + cos (x) sin (x) csc (x)

= cos (x) sin (x) tan (x) + cos (x) sin (x) csc (x)

簡素化

cos (x) sin (x) tan (x) + cos (x) sin (x) csc (x) : sin (x) (cot (x) + sin (x))

= sin (x) (cot (x) + sin (x))

分配法則を適用する:

a (b + c) = ab + a c

sin (x) (cot (x) + sin (x)) = sin (x) cot (x) + sin (x) sin (x)

= sin (x) cot (x) + sin (x) sin (x)

簡素化

sin (x) cot (x) + sin (x) sin (x) : cot (x) sin (x) + sin^{2} (x)

= cot (x) sin (x) + sin^{2} (x)