Question

The general solution of cosec x = `-sqrt2` is ______ 

Options

• `x = npi ± pi/6, n ∈ Z`

• `x = 2npi ± pi/6, n ∈ Z`

• `x = npi + (-1)^n (pi/4), n ∈ Z`

• `x = npi + (-1)^n ((5pi)/4), n ∈ Z`

Answer 1

The general solution of cosec x = `-sqrt2` is `underline(x = npi + (-1)^n ((5pi)/4), n ∈ Z)`.

Explanation:

cosec x = `-sqrt2`

⇒ `sinx = -1/sqrt2`

⇒ `sinx = -sin(pi/4) = sin(pi + pi/4) = sin((5pi)/4)`

⇒ `x = npi + (-1)^n ((5pi)/4), n ∈ Z` ...............[∵ sin θ = sin α ⇒ θ = nπ(-1)ⁿ α]