Question

Please HELP!! Find all the solutions of the given equation: csc θ − cot θ = sin θ
I've got the cosθ=0 and cosθ=1

Answer 1

csc θ − cot θ = sin θ
(1-cosθ )/sin θ = sin θ
1-cosθ= sin^2 θ
1-cosθ = 1- cos^2 θ
(1-cosθ) = (1-cosθ)*(1+cosθ)
(1-cosθ)*(1+cosθ-1)=0
so cosθ=0 and cosθ=1 which u have got is right

Answer 2

Now cosθ=0 whenever θ is an odd integral multiple of pi/2
and cosθ=1 whenever θ is an even integral multiple of pi

Answer 3

so the θ=pi/2+2kpi and θ=pi+2kpi? @matricked

Answer 4

θ=2kpi +- pi/2 (or θ=pi/2+2kpi )

and θ=2kpi