Question

Solve 2sin ^2x-sin x-1=0

Answer 1

The equation 2sin^2x - sin x - 1 = 0 is treated as a quadratic equation by substituting sin x with a variable, then solved using the quadratic formula to find sin x, and finally taking the inverse sine to obtain the values for x.

Step-by-step explanation:

To solve the trigonometric equation 2sin^2x - sin x - 1 = 0, we can treat it as a quadratic equation by substituting sin x with a variable, let's say 'u'. So, the equation becomes 2u^2 - u - 1 = 0.

We can solve this quadratic equation using the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / (2a), where in our case, a = 2, b = -1, and c = -1.

By substituting these values into the quadratic formula, we determine the solutions for 'u', which represent the values of sin x. After finding 'u', we take the inverse sine to find the possible values of x within the defined domain of the sine function.

To finalize, we substitute back sin x for 'u' and obtain the values of x that solve the original equation.

Answer 2

Consider, pls, the suggested solution.

Answer:

`\left[\begin{array}{ccc}x=(-1)^(n+1)* ( \pi)/(6) + \pi n\\ \ x= ( \pi)/(2) +2 \pi n\end{array}`