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Popular >

sec(θ)csc(θ)+sqrt(2)csc(θ)=0

Solution

sec (θ) csc (θ) + 2 csc (θ) = 0

Solution

θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

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Solution steps

sec (θ) csc (θ) + 2 csc (θ) = 0

Factor

sec (θ) csc (θ) + 2 csc (θ) : csc (θ) (sec (θ) + 2)

csc (θ) (sec (θ) + 2) = 0

Solving each part separately

csc (θ) = 0 or sec (θ) + 2 = 0

csc (θ) = 0 :

No Solution

sec (θ) + 2 = 0 : θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

Combine all the solutions

θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

Popular Examples

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2 sin (x) + cos (x) = 1

sin(θ)cos(θ)=-1/2

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Frequently Asked Questions (FAQ)

What is the general solution for sec(θ)csc(θ)+sqrt(2)csc(θ)=0 ?
The general solution for sec(θ)csc(θ)+sqrt(2)csc(θ)=0 is θ=(3pi)/4+2pin,θ=(5pi)/4+2pin