证明 (1-cos^2(x))/(1+sin(x))=sin(x)

解答

证明

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

假

求解步骤

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

两侧不相等

对于

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

代入

x = 1

\frac{1 - cos ^{2} ( 1 )}{1 + sin ( 1 )} = 0.38451 \dots

\frac{1 - cos ^{2} ( 1 )}{1 + sin ( 1 )}

整理为小数形式

= 0.38451 \dots

sin (1) = 0.84147 \dots

sin (1)

整理为小数形式

= 0.84147 \dots

两侧不相等

\Rightarrow 假

p ro v e cos (θ) \cdot tan (θ) \cdot csc (θ) = 1

p ro v e \frac{1}{2} cot (\frac{x}{2}) - \frac{1}{2} tan (\frac{x}{2}) = cot (x)

p ro v e \frac{- cot ( x ) + 1}{tan ( x ) - 1} = cot (x)

p ro v e 4 cos^{2} (a) + 4 sin^{2} (a) = 4

p ro v e \frac{sin ( a )}{tan ( a )} = cos (a)