证明 (cot^3(t))/(csc(t))=cos(t)(csc^2(-1))

解答

证明

\frac{cot ^{3} ( t )}{csc ( t )} = cos (t) (csc^{2} (- 1))

假

求解步骤

\frac{cot ^{3} ( t )}{csc ( t )} = cos (t) csc^{2} (- 1)

两侧不相等

对于

\frac{cot ^{3} ( t )}{csc ( t )} = cos (t) csc^{2} (- 1)

代入

t = 1

\frac{cot ^{3} ( 1 )}{csc ( 1 )} = 0.22275 \dots

\frac{cot ^{3} ( 1 )}{csc ( 1 )}

整理为小数形式

= 0.22275 \dots

cos (1) csc^{2} (- 1) = 0.76305 \dots

cos (1) csc^{2} (- 1)

整理为小数形式

= 0.76305 \dots

两侧不相等

\Rightarrow 假

p ro v e \frac{sec ^{2} ( x ) cot ( x )}{csc ^{2} ( x )} = tan (x)

p ro v e \frac{sec ^{2} ( y )}{tan ( y )} = tan (y) + cot (y)

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

p ro v e tan (x - 36 0^{\circ}) = tan (x)

p ro v e cos^{2} (x) - 1 = - sin^{2} (x)