证明 sin(a)csc(a)=1

解答

证明

sin (a) csc (a) = 1

真

求解步骤

sin (a) csc (a) = 1

调整左侧

sin (a) csc (a)

csc (a) sin (a) = 1

csc (a) sin (a)

用 sin, cos 表示

csc (a) sin (a)

使用基本三角恒等式:

csc (a) = \frac{1}{sin ( a )}

= \frac{1}{sin ( a )} sin (a)

\frac{1}{sin ( a )} sin (a) = 1

\frac{1}{sin ( a )} sin (a)

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 sin ( a )}{sin ( a )}

约分:

sin (a)

= 1

= 1

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

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

p ro v e cos (33 0^{\circ}) = 1 - 2 sin^{2} (16 5^{\circ})

p ro v e tan^{4} (x) = sec^{4} (x) - sec^{2} (x)

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

p ro v e (1 - tan^{2} (θ)) = sec^{2} (θ) - 4 tan^{2} (θ)