证明 sin^2(x)(1+(cos(x))/(sin(x)))=1

解答

证明

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

假

求解步骤

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

两侧不相等

对于

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

代入

x = 1

sin^{2} (1) (1 + \frac{cos ( 1 )}{sin ( 1 )}) = 1.16272 \dots

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

整理为小数形式

= 1.16272 \dots

两侧不相等

\Rightarrow 假

p ro v e tan (x) + 1 = 1

p ro v e cos (k (x) x) = cos (- k (x) x)

p ro v e tan^{2} (x) = sin^{2} (x) + sin^{2} (x) tan^{2} (x)

p ro v e - sin (x) sec (x) = - tan (x)

p ro v e cos (4 x) - cos (3 x) cos (x) = sin (2 x) - 4 cos (2 x) sin (2 x)