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 (2sin(x)cos(x)sec(x))/2 =sin(x)

解答

证明

\frac{2 sin ( x ) cos ( x ) sec ( x )}{2} = sin (x)

解答

真

求解步骤

\frac{2 sin ( x ) cos ( x ) sec ( x )}{2} = sin (x)

调整左侧

\frac{2 sin ( x ) cos ( x ) sec ( x )}{2}

用 sin, cos 表示

\frac{2 cos ( x ) sec ( x ) sin ( x )}{2}

使用基本三角恒等式:

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

= \frac{2 cos ( x ) \frac{1}{c o s ( x )} sin ( x )}{2}

化简

\frac{2 cos ( x ) \frac{1}{c o s ( x )} sin ( x )}{2} : sin (x)

\frac{2 cos ( x ) \frac{1}{c o s ( x )} sin ( x )}{2}

乘

2 cos (x) \frac{1}{cos ( x )} sin (x) : 2 sin (x)

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

分式相乘:

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

= \frac{1 \cdot 2 cos ( x ) sin ( x )}{cos ( x )}

约分:

cos (x)

= 1 \cdot 2 sin (x)

数字相乘:

1 \cdot 2 = 2

= 2 sin (x)

= \frac{2 sin ( x )}{2}

数字相除:

\frac{2}{2} = 1

= sin (x)

= sin (x)

= sin (x)

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^2(x)+tan^2(x)cos^2(x)=sin(x)

p ro v e cos^{2} (x) + tan^{2} (x) cos^{2} (x) = sin (x)

证明 (-csc(x))/(sec(x))+(cos(x))/(-sin(x))=-2cot(x)

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

证明 1+tan^2(3/4)=sec^2(x)

p ro v e 1 + tan^{2} (\frac{3}{4}) = sec^{2} (x)

证明 sin((3pi)/4)= 1/(sqrt(2))

p ro v e sin (\frac{3 π}{4}) = \frac{1}{2}

证明 sin(c)=2sin(c/2)cos(c/2)

p ro v e sin (c) = 2 sin (\frac{c}{2}) cos (\frac{c}{2})