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受欢迎的三角函数 >

证明 (cot(x))(sec(x))(sin(x))=1

解答

证明

(cot (x)) (sec (x)) (sin (x)) = 1

解答

真

求解步骤

cot (x) sec (x) sin (x) = 1

调整左侧

cot (x) sec (x) sin (x)

用 sin, cos 表示

cot (x) sec (x) sin (x)

使用基本三角恒等式:

cot (x) = \frac{cos ( x )}{sin ( x )}

= \frac{cos ( x )}{sin ( x )} sec (x) sin (x)

使用基本三角恒等式:

sec (x) = \frac{1}{cos ( x )}

= \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )} sin (x)

\frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )} sin (x) = 1

\frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )} sin (x)

分式相乘:

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

= \frac{cos ( x ) \cdot 1 \cdot sin ( x )}{sin ( x ) cos ( x )}

约分:

cos (x)

= \frac{1 \cdot sin ( x )}{sin ( x )}

约分:

sin (x)

= 1

= 1

= 1

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

流行的例子

证明 (cos(a))/(1-sin(a))-tan(a)=sec(a)

p ro v e \frac{cos ( a )}{1 - sin ( a )} - tan (a) = sec (a)

证明 tan(θ/2)+cot(θ/2)=2csc(θ)

p ro v e tan (\frac{θ}{2}) + cot (\frac{θ}{2}) = 2 csc (θ)

证明 sin^2(2θ)=4sin^2(θ)cos^2(θ)

p ro v e sin^{2} (2 θ) = 4 sin^{2} (θ) cos^{2} (θ)

证明 (cos(4x)+cos(6x))/(sin(4x)-sin(6x))=-cot(x)

p ro v e \frac{cos ( 4 x ) + cos ( 6 x )}{sin ( 4 x ) - sin ( 6 x )} = - cot (x)

证明 2sin^2(x)=(1-cos(2x))

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