证明 cos^3(x)=(1-sin^2(x))(cos(x))

解答

证明

cos^{3} (x) = (1 - sin^{2} (x)) (cos (x))

真

求解步骤

cos^{3} (x) = (1 - sin^{2} (x)) cos (x)

调整右侧

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

使用三角恒等式改写

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

使用毕达哥拉斯恒等式:

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

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

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

化简

cos^{2} (x) cos (x) : cos^{3} (x)

cos^{2} (x) cos (x)

使用指数法则:

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

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

= cos^{2 + 1} (x)

数字相加:

2 + 1 = 3

= cos^{3} (x)

= cos^{3} (x)

= cos^{3} (x)

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

p ro v e tan (3 x) cos (3 x) = sin (3 x)

p ro v e 9 cos^{2} (x) - 9 sin^{2} (x) = 9 - 18 sin^{2} (x)

p ro v e 7 cos^{2} (B) - 7 sin^{2} (B) = 14 cos^{2} (B) - 7

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

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