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受欢迎的三角函数 >

sec(x)csc(x)=sqrt(2)sec(x)

解答

sec (x) csc (x) = 2 sec (x)

解答

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

+1

度数

x = 4 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n

求解步骤

sec (x) csc (x) = 2 sec (x)

两边减去

2 sec (x)

sec (x) csc (x) - 2 sec (x) = 0

分解

sec (x) csc (x) - 2 sec (x) : sec (x) (csc (x) - 2)

sec (x) csc (x) - 2 sec (x)

因式分解出通项

sec (x)

= sec (x) (csc (x) - 2)

sec (x) (csc (x) - 2) = 0

分别求解每个部分

sec (x) = 0 or csc (x) - 2 = 0

sec (x) = 0 :

无解

sec (x) = 0

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

无解

csc (x) - 2 = 0 : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

csc (x) - 2 = 0

将

2

到右边

csc (x) - 2 = 0

两边加上

2

csc (x) - 2 + 2 = 0 + 2

化简

csc (x) = 2

csc (x) = 2

csc (x) = 2

的通解

csc (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

合并所有解

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

作图

流行的例子

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

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

(tan(θ)-1)(cos(θ)-1)=0

(tan (θ) - 1) (cos (θ) - 1) = 0

cos (x) = \frac{16}{20}

cos(2x)+10sin^2(x)=7

cos (2 x) + 10 sin^{2} (x) = 7

cos(x)=-sqrt(3)

cos (x) = - 3