证明 sin(θ)(cos^2(θ))/(sin(θ))=csc(θ)

解答

证明

sin (θ) \frac{cos ^{2} ( θ )}{sin ( θ )} = csc (θ)

假

求解步骤

sin (θ) \frac{cos ^{2} ( θ )}{sin ( θ )} = csc (θ)

两侧不相等

对于

sin (θ) \frac{cos ^{2} ( θ )}{sin ( θ )} = csc (θ)

代入

θ = 1

sin (1) \frac{cos ^{2} ( 1 )}{sin ( 1 )} = 0.29192 \dots

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

整理为小数形式

= 0.29192 \dots

csc (1) = 1.18839 \dots

csc (1)

整理为小数形式

= 1.18839 \dots

两侧不相等

\Rightarrow 假

p ro v e \frac{tan ^{2} ( a ) + 1}{sec ( a )} = sec (a)

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

p ro v e cos (30 0^{\circ}) = 1 - 2 sin^{2} (15 0^{\circ})

p ro v e csc^{2} (x) + 3 cot^{2} (x) - 5 = 4 (cot (x) - 1)

p ro v e (3) \frac{( cos ( 2 z ) ) ^{2}}{2} = \frac{3 cos ( 4 z )}{4}