簡約 (sin(x)+csc(x))^2+(cos(x)+sec(x))^2

解

簡約

(sin (x) + csc (x))^{2} + (cos (x) + sec (x))^{2}

csc^{2} (x) + sec^{2} (x) + 5

解答ステップ

(sin (x) + csc (x))^{2} + (cos (x) + sec (x))^{2}

拡張

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

= csc^{2} (x) + sin^{2} (x) + 2 + (cos (x) + sec (x))^{2}

拡張

(cos (x) + sec (x))^{2} : cos^{2} (x) + 2 cos (x) sec (x) + sec^{2} (x)

= csc^{2} (x) + sin^{2} (x) + 2 + cos^{2} (x) + 2 cos (x) sec (x) + sec^{2} (x)

ピタゴラスの公式を使用する:

cos^{2} (x) + sin^{2} (x) = 1

= csc^{2} (x) + sec^{2} (x) + 2 cos (x) sec (x) + 2 + 1

数を足す:

2 + 1 = 3

= csc^{2} (x) + sec^{2} (x) + 2 cos (x) sec (x) + 3

sec (x) cos (x) = 1

= csc^{2} (x) + sec^{2} (x) + 3 + 2 \cdot 1

数を乗じる:

2 \cdot 1 = 2

= csc^{2} (x) + sec^{2} (x) + 3 + 2

数を足す:

3 + 2 = 5

= csc^{2} (x) + sec^{2} (x) + 5