证明 cos^2(t)=((1+cos(2t)))/2

解答

证明

cos^{2} (t) = \frac{( 1 + cos ( 2 t ) )}{2}

真

求解步骤

cos^{2} (t) = \frac{1 + cos ( 2 t )}{2}

调整右侧

\frac{1 + cos ( 2 t )}{2}

使用三角恒等式改写

\frac{1 + cos ( 2 t )}{2}

使用倍角公式:

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

= \frac{1 + 2 cos ^{2} ( t ) - 1}{2}

化简

\frac{1 + 2 cos ^{2} ( t ) - 1}{2} : cos^{2} (t)

\frac{1 + 2 cos ^{2} ( t ) - 1}{2}

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

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

对同类项分组

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

1 - 1 = 0

= 2 cos^{2} (t)

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

数字相除:

\frac{2}{2} = 1

= cos^{2} (t)

= cos^{2} (t)

= cos^{2} (t)

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

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