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Question
Find the general solution of the following equation:
cosec θ = - √2.
Solution
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.
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