证明 1/(sin^2(x)tan(x))=-sec(x)

解答

证明

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

假

求解步骤

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

两侧不相等

对于

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

代入

x = 1

\frac{1}{sin ^{2} ( 1 ) tan ( 1 )} = 0.90681 \dots

\frac{1}{sin ^{2} ( 1 ) tan ( 1 )}

整理为小数形式

= 0.90681 \dots

- sec (1) = - 1.85081 \dots

- sec (1)

整理为小数形式

= - 1.85081 \dots

两侧不相等

\Rightarrow 假

p ro v e cot^{2} (x) = - 1 + csc^{2} (x)

p ro v e sin (2 x) - cos (2 x) = tan (2 x) - 1

p ro v e (tan (θ) + cot (θ)) sin (θ) cos (θ) = 1

p ro v e 3 (tan (x)) + 12 = 3

p ro v e 2 cos (x) tan (x) cot (x) = 2