Question

Find the principal solutions of each of the following equations :

(i) sin x = -1/2

(ii)  √2 cos x + 1 = 0

(iii) tan x = -1

Answer 1

To Find: Principal solution.

(i) Given: sin x = -1/2

Formula used: sin θ = sinα 

⇒ θ = nπ + (-1)ⁿ α , n ∈ l

By using formula, we have

(ii) Given:  √2 cos x + = 0 

⇒ cos x = -1/√2

Formula used: cos θ = cos α 

⇒ θ = 2nπ ± α , n ∈ l

By using formula, we have

so principal solution is x = 3π/4 and 5π/4

(iii) Given: tan x = -1

Formula used: tan θ = cos α 

⇒ θ = 2nπ ± α , n ∈ l

By using formula, we have