zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

证明 sec(y)-cos(y)=tan(y)sin(y)

解答

证明

sec (y) - cos (y) = tan (y) sin (y)

解答

真

求解步骤

sec (y) - cos (y) = tan (y) sin (y)

调整左侧

sec (y) - cos (y)

用 sin, cos 表示

- cos (y) + sec (y)

使用基本三角恒等式:

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

= - cos (y) + \frac{1}{cos ( y )}

化简

- cos (y) + \frac{1}{cos ( y )} : \frac{- cos ^{2} ( y ) + 1}{cos ( y )}

- cos (y) + \frac{1}{cos ( y )}

将项转换为分式:

cos (y) = \frac{cos ( y ) cos ( y )}{cos ( y )}

= - \frac{cos ( y ) cos ( y )}{cos ( y )} + \frac{1}{cos ( y )}

因为分母相等，所以合并分式:

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

= \frac{- cos ( y ) cos ( y ) + 1}{cos ( y )}

- cos (y) cos (y) + 1 = - cos^{2} (y) + 1

- cos (y) cos (y) + 1

cos (y) cos (y) = cos^{2} (y)

cos (y) cos (y)

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

cos (y) cos (y) = cos^{1 + 1} (y)

= cos^{1 + 1} (y)

数字相加:

1 + 1 = 2

= cos^{2} (y)

= - cos^{2} (y) + 1

= \frac{- cos ^{2} ( y ) + 1}{cos ( y )}

= \frac{- cos ^{2} ( y ) + 1}{cos ( y )}

= \frac{1 - cos ^{2} ( y )}{cos ( y )}

调整右侧

tan (y) sin (y)

用 sin, cos 表示

sin (y) tan (y)

使用基本三角恒等式:

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

= sin (y) \frac{sin ( y )}{cos ( y )}

化简

sin (y) \frac{sin ( y )}{cos ( y )} : \frac{sin ^{2} ( y )}{cos ( y )}

sin (y) \frac{sin ( y )}{cos ( y )}

分式相乘:

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

= \frac{sin ( y ) sin ( y )}{cos ( y )}

sin (y) sin (y) = sin^{2} (y)

sin (y) sin (y)

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

sin (y) sin (y) = sin^{1 + 1} (y)

= sin^{1 + 1} (y)

数字相加:

1 + 1 = 2

= sin^{2} (y)

= \frac{sin ^{2} ( y )}{cos ( y )}

= \frac{sin ^{2} ( y )}{cos ( y )}

= \frac{sin ^{2} ( y )}{cos ( y )}

使用三角恒等式改写

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

使用毕达哥拉斯恒等式:

cos^{2} (x) + sin^{2} (x) = 1

sin^{2} (x) = 1 - cos^{2} (x)

= \frac{1 - cos ^{2} ( y )}{cos ( y )}

= \frac{1 - cos ^{2} ( y )}{cos ( y )}

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 sin(5x)-sin(3x)=2cos(4x)sin(x)

p ro v e sin (5 x) - sin (3 x) = 2 cos (4 x) sin (x)

证明 sin(40)=2sin(20)cos(20)

p ro v e sin (4 0^{\circ}) = 2 sin (2 0^{\circ}) cos (2 0^{\circ})

证明 sin(θ)-cos^2(θ)sin(θ)=sin^3(θ)

p ro v e sin (θ) - cos^{2} (θ) sin (θ) = sin^{3} (θ)

证明 sec^2(x)+csc^2(x)=(sec(x)csc(x))^2

p ro v e sec^{2} (x) + csc^{2} (x) = (sec (x) csc (x))^{2}

证明 (1+sin(x))/(sin(x))=1+csc(x)

p ro v e \frac{1 + sin ( x )}{sin ( x )} = 1 + csc (x)