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 cos^2(B)-sin^2(B)=2cos^2(B)-1

解答

证明

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

解答

真

求解步骤

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

调整左侧

cos^{2} (B) - sin^{2} (B)

使用三角恒等式改写

cos^{2} (B) - sin^{2} (B)

使用毕达哥拉斯恒等式:

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

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

= cos^{2} (B) - (1 - cos^{2} (B))

化简

cos^{2} (B) - (1 - cos^{2} (B)) : 2 cos^{2} (B) - 1

cos^{2} (B) - (1 - cos^{2} (B))

- (1 - cos^{2} (B)) : - 1 + cos^{2} (B)

- (1 - cos^{2} (B))

打开括号

= - (1) - (- cos^{2} (B))

使用加减运算法则

- (- a) = a, - (a) = - a

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

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

化简

cos^{2} (B) - 1 + cos^{2} (B) : 2 cos^{2} (B) - 1

cos^{2} (B) - 1 + cos^{2} (B)

对同类项分组

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

同类项相加:

cos^{2} (B) + cos^{2} (B) = 2 cos^{2} (B)

= 2 cos^{2} (B) - 1

= 2 cos^{2} (B) - 1

= 2 cos^{2} (B) - 1

= 2 cos^{2} (B) - 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 csc^2(x)cos^2(x)= 1/(tan^2(x))

p ro v e csc^{2} (x) cos^{2} (x) = \frac{1}{tan ^{2} ( x )}

证明 1+tan^2(t)=sec^2(t)

p ro v e 1 + tan^{2} (t) = sec^{2} (t)

证明 cos(4x)=2cos^2(2x)-1

p ro v e cos (4 x) = 2 cos^{2} (2 x) - 1

证明 sin(x)sec(x)= 1/(cos(x)csc(x))

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

证明 (1+tan^2(x))cos(x)=sec(x)

p ro v e (1 + tan^{2} (x)) cos (x) = sec (x)