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受欢迎的三角函数 >

证明 25sec^2(5x)=25+25tan^2(5x)

解答

证明

25 sec^{2} (5 x) = 25 + 25 tan^{2} (5 x)

解答

真

求解步骤

25 sec^{2} (5 x) = 25 + 25 tan^{2} (5 x)

调整右侧

25 + 25 tan^{2} (5 x)

使用三角恒等式改写

25 + 25 tan^{2} (5 x)

使用毕达哥拉斯恒等式:

tan^{2} (x) + 1 = sec^{2} (x)

tan^{2} (x) = sec^{2} (x) - 1

= 25 + 25 (sec^{2} (5 x) - 1)

化简

25 + 25 (sec^{2} (5 x) - 1) : 25 sec^{2} (5 x)

25 + 25 (sec^{2} (5 x) - 1)

乘开

25 (sec^{2} (5 x) - 1) : 25 sec^{2} (5 x) - 25

25 (sec^{2} (5 x) - 1)

使用分配律:

a (b - c) = ab - a c

a = 25, b = sec^{2} (5 x), c = 1

= 25 sec^{2} (5 x) - 25 \cdot 1

数字相乘:

25 \cdot 1 = 25

= 25 sec^{2} (5 x) - 25

= 25 + 25 sec^{2} (5 x) - 25

化简

25 + 25 sec^{2} (5 x) - 25 : 25 sec^{2} (5 x)

25 + 25 sec^{2} (5 x) - 25

对同类项分组

= 25 sec^{2} (5 x) + 25 - 25

25 - 25 = 0

= 25 sec^{2} (5 x)

= 25 sec^{2} (5 x)

= 25 sec^{2} (5 x)

= 25 sec^{2} (5 x)

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

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