证明 arcsin(x)=csc(x)

解答

证明

arcsin (x) = csc (x)

假

求解步骤

arcsin (x) = csc (x)

两侧不相等

对于

arcsin (x) = csc (x)

代入

x = 1

arcsin (1) = \frac{π}{2} (Decimal : Degrees : 1.57079 \dots 9 0^{\circ})

arcsin (1)

使用以下普通恒等式:

arcsin (1) = \frac{π}{2}

arcsin (1)

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= \frac{π}{2}

= \frac{π}{2}

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 cos^{4} (A) - sin^{4} (A) = cos (2 A)

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

p ro v e tan (θ) + 1 = sec (θ)

p ro v e cos (θ) sec (θ) - cos^{2} (θ) = sin^{2} (θ)

p ro v e sin (12 x) = 2 sin (6 x) cos (6 x)