Question

Solve for x,
2 sin^2 x - sin x = 0
SRSLY, I NEED HELP!!!

Answer 1

Answer:

Given that,

• 2 Sin²x - Sinx = 0

To find,

• x = ?

Solution,

→ 2 Sin²x - Sinx = 0

Taking, (Sin x) commonly outside, we get:

→ Sin x ( 2 Sin x - 1 ) = 0

→ Sin x = 0 ; ( 2 Sin x - 1 ) = 0

Case (i) :- Sin x = 0

→ x = 0, π. 2π, ...

Hence the principle solution of Sin x = 0 is { 0, π, 2π }.

The general solution of Sin x = 0 is nπ, where n ∈ Z ( Z = integers ).

Case (ii) :- ( 2 Sin x - 1 ) = 0

→ 2 Sin x = 1

→ Sin x = 1/2

→ x = π/6, 5π/6, 13π/6, ...

Hence the principal solution of Sin x = 1/2 is { π/6, 5π/6 }.

The general solution of Sin x = 1/2 is { 2nπ + π/6 }, where n ∈ Z.

Considering the principal solutions, we get:

Solution Set of x = { 0, π/6, 5π/6, π, 2π }