Question

general solution of cosec(theta/2)=-1​

Answer 1

Answer:

Step-by-step explanation:

The solution is as follows

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Answer 2

The general solution of 'θ' for the equation cosec (θ/2) = -1 is given by:

θ = 2nπ - (-1)ⁿ(π) where n∈Integers.

Given:

Equation: cosec (θ/2) = -1

To Find:

The general solution for the value of 'θ' in the equation: cosec (θ/2) = -1

Solution:

                               ∵ cosec (θ/2) = -1

                                ∴ sin (θ/2) = -1

→ As we know that sin(-π/2) = -1

                                ∴ sin(θ/2) = sin(-π/2)

→ For a general equation sinΦ = sinα, the general solution for 'Φ' is given by:

                    Φ = nπ + (-1)ⁿα where n∈Integers and α∈[-π/2 , π/2]      

       

∴ For the equation sin(θ/2) = sin(-π/2), the general solution is given by:

                                  → (θ/2) = nπ + (-1)ⁿ(-π/2) where n∈Integers

                                    → θ = 2nπ - (-1)ⁿ(π) where n∈Integers

Hence the general solution of 'θ' for the equation cosec (θ/2) = -1 is given by:

                              θ = 2nπ - (-1)ⁿ(π) where n∈Integers

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