证明 1-(cos^2(x))/(1+sin^2(x))=sin(x)

解答

证明

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

假

求解步骤

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

两侧不相等

对于

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

代入

x = 1

1 - \frac{cos ^{2} ( 1 )}{1 + sin ^{2} ( 1 )} = 0.82909 \dots

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

整理为小数形式

= 0.82909 \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 \frac{1}{2} sec (x) - 1 = 0

p ro v e \frac{cos ( 2 x ) + 1}{2} = cos^{2} (x)

p ro v e cos^{3} (A) = \frac{1}{4} (cos (3 A) + 3 cos (A))

p ro v e \frac{1}{sin ( x ) + 1} + \frac{1}{csc ( + 1 )} = 1

p ro v e cot (- θ) = - cot (θ)