证明 sin^4(x)=(1-cos^2(x))^2

解答

证明

sin^{4} (x) = (1 - cos^{2} (x))^{2}

真

求解步骤

sin^{4} (x) = (1 - cos^{2} (x))^{2}

调整右侧

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

使用三角恒等式改写

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

使用毕达哥拉斯恒等式:

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

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

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

化简

(sin^{2} (x))^{2} : sin^{4} (x)

(sin^{2} (x))^{2}

使用指数法则:

(a^{b})^{c} = a^{b c}

= sin^{2 \cdot 2} (x)

数字相乘:

2 \cdot 2 = 4

= sin^{4} (x)

= sin^{4} (x)

= sin^{4} (x)

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

p ro v e \frac{4}{cos ^{2} ( x )} - 5 = 4 tan^{2} (x) - 1

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

p ro v e 25 sin^{2} (x) + 25 cos^{2} (x) = 25

p ro v e cot (x) sin (x) sec (x) = 1

p ro v e \frac{1}{1 - cos ( x )} - \frac{1}{1 + cos ( x )} = 2 cot (x) csc (x)