簡約 (cos(x)+sec(x))^2+sin^2(x)-tan^2(x)+3

解

簡約

(cos (x) + sec (x))^{2} + sin^{2} (x) - tan^{2} (x) + 3

7

解答ステップ

(cos (x) + sec (x))^{2} + sin^{2} (x) - tan^{2} (x) + 3

拡張

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

= cos^{2} (x) + 2 cos (x) sec (x) + sec^{2} (x) + sin^{2} (x) - tan^{2} (x) + 3

ピタゴラスの公式を使用する:

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

= sec^{2} (x) + 2 cos (x) sec (x) - tan^{2} (x) + 3 + 1

数を足す:

3 + 1 = 4

= sec^{2} (x) + 2 cos (x) sec (x) - tan^{2} (x) + 4

ピタゴラスの公式を使用する:

sec^{2} (x) = tan^{2} (x) + 1

sec^{2} (x) - tan^{2} (x) = 1

= 2 cos (x) sec (x) + 4 + 1

数を足す:

4 + 1 = 5

= 2 cos (x) sec (x) + 5

sec (x) cos (x) = 1

= 5 + 2 \cdot 1

数を乗じる:

2 \cdot 1 = 2

= 5 + 2

数を足す:

5 + 2 = 7

= 7