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人気のある三角関数 >

証明する (cos(x)sec(x))/(tan(x))=cot(x)

解

証明する

\frac{cos ( x ) sec ( x )}{tan ( x )} = cot (x)

解

真

解答ステップ

\frac{cos ( x ) sec ( x )}{tan ( x )} = cot (x)

左側を操作する

\frac{cos ( x ) sec ( x )}{tan ( x )}

サイン, コサインで表わす

\frac{cos ( x ) sec ( x )}{tan ( x )}

基本的な三角関数の公式を使用する:

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

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

基本的な三角関数の公式を使用する:

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

= \frac{cos ( x ) \frac{1}{c o s ( x )}}{\frac{s i n ( x )}{c o s ( x )}}

簡素化

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

\frac{cos ( x ) \frac{1}{c o s ( x )}}{\frac{s i n ( x )}{c o s ( x )}}

分数の規則を適用する:

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

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

cos (x) \frac{1}{cos ( x )} cos (x) = \frac{1}{cos ( x )} cos^{2} (x)

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

指数の規則を適用する:

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

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

= \frac{1}{cos ( x )} cos^{1 + 1} (x)

数を足す:

1 + 1 = 2

= \frac{1}{cos ( x )} cos^{2} (x)

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

乗じる

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

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

分数を乗じる:

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

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

乗算:

1 \cdot cos^{2} (x) = cos^{2} (x)

= \frac{cos ^{2} ( x )}{cos ( x )}

共通因数を約分する:

cos (x)

= cos (x)

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

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

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

基本的な三角関数の公式を使用する:

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

= cot (x)

両辺を同じ形式にできることを証明した

\Rightarrow 真

人気の例

証明する (csc^2(t))/(cot(t))=csc(t)sec(t)

p ro v e \frac{csc ^{2} ( t )}{cot ( t )} = csc (t) sec (t)

証明する (2cos(2x))/(sin(2x))=cot(x)-tan(x)

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

証明する cot^2(t)-cos^2(t)=cot^2(t)cos^2(t)

p ro v e cot^{2} (t) - cos^{2} (t) = cot^{2} (t) cos^{2} (t)

証明する cot(θ)=(cos(θ))/(sin(θ))

p ro v e cot (θ) = \frac{cos ( θ )}{sin ( θ )}

証明する (1-cot(x))^2=csc^2(x)-2cot(x)

p ro v e (1 - cot (x))^{2} = csc^{2} (x) - 2 cot (x)