证明 sin^4(x)=(sin^2(x))^2

解答

证明

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

真

求解步骤

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

调整右侧

(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)

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

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

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

p ro v e 1 - 2 sin^{2} (y) + sin^{4} (y) = cos^{4} (y)

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

p ro v e (1 - sin (3 a)) (sin (3 a) + 1) = cos^{2} (3 a)