Question

Find the general solution of the following equation:

cosec θ = - √2.

Answer 1

The general solution of sin θ = sin α is

θ = nπ + (–1)ⁿα, n ∈ Z.

Now,

Cosec θ = - √2

∴ sin θ = `- (1)/sqrt(2)`        

∴ sin θ = `-sin  pi/(4)               ...[∵ sin  pi/(4) = (1)/sqrt(2)]` 

∴ sin θ = `sin(pi + pi/4)`    ...[ ∵ sin(π + θ) = – sin θ] 

∴ sinθ = `sin  (5pi)/(4)`         

∴ the required general solution is
θ = nπ + (-1)ⁿ `((5pi)/4)`, n ∈ Z.