证明 1/(sin^2(x))= 1/(csc^2(x))

解答

证明

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

假

求解步骤

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

两侧不相等

对于

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

代入

x = 1

\frac{1}{sin ^{2} ( 1 )} = 1.41228 \dots

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

整理为小数形式

= 1.41228 \dots

\frac{1}{csc ^{2} ( 1 )} = 0.70807 \dots

\frac{1}{csc ^{2} ( 1 )}

整理为小数形式

= 0.70807 \dots

两侧不相等

\Rightarrow 假

p ro v e sin (x) (1 + tan^{2} (x)) = sin (x) sec^{2} (x)

p ro v e \frac{tan ^{2} ( X )}{1 + cot ^{2} ( X )} = sin^{4} (X)

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

p ro v e 1 + cos (6 x) = 2 cos^{2} (3 x)

p ro v e \frac{sec ( a )}{cot ( a ) + tan ( a )} = sin (a)