证明 (1-tan^2(x))/(1+tan^2(x))=sec(x)

解答

证明

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

假

求解步骤

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

两侧不相等

对于

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

代入

x = 1

\frac{1 - tan ^{2} ( 1 )}{1 + tan ^{2} ( 1 )} = - 0.41614 \dots

\frac{1 - tan ^{2} ( 1 )}{1 + tan ^{2} ( 1 )}

整理为小数形式

= - 0.41614 \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 2 sec (x) = 2 + 2 tan (x)

p ro v e sin^{2} (θ) (1 + cos^{2} (θ)) = 1

p ro v e sin (x) tan (x) = cos (x)

p ro v e 2 sin^{2} (\frac{x}{2}) + 4 cos^{2} (\frac{x}{2}) - 3 = cos (x)

p ro v e tan (2 u) = \frac{( 2 tan ( u ) )}{1 - tan ^{2} ( u )}