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受欢迎的三角函数 >

(1+tan(x))^2+(1-tan(x))^2=sec^2(x)

解答

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

解答

x \in R 无解

求解步骤

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

两边减去

sec^{2} (x)

2 tan^{2} (x) - sec^{2} (x) + 2 = 0

使用三角恒等式改写

2 - sec^{2} (x) + 2 tan^{2} (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

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

化简

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

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

乘开

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

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

使用分配律:

a (b - c) = ab - a c

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

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

数字相乘:

2 \cdot 1 = 2

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

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

化简

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

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

同类项相加:

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

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

对同类项分组

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

2 - 2 = 0

= sec^{2} (x)

= sec^{2} (x)

= sec^{2} (x)

sec^{2} (x) = 0

使用法则

x^{n} = 0 \Rightarrow x = 0

sec (x) = 0

sec (x) \leq - 1 or sec (x) \geq 1

x \in R 无解

作图

流行的例子

tan(x)=-(sqrt(2))/2

tan (x) = - \frac{2}{2}

cot (x) = 1.2

tan (x) = \frac{30}{100}

sec(x)-tan(x)=2

sec (x) - tan (x) = 2

sin((2pi(t+101.75))/(365))=-1

sin (\frac{2 π ( t + 101.75 )}{365}) = - 1