Question

Solve the equation. Give a general formula for all the solutions | 2 sin x - 2 =0 Give a general formula for all the solutions by using angle(s) in the interval [0.2x), and adding multiples of some integer n. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. x= (Simplify your answer. Type an exact answer, using x as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed.) OB. There is no solution

Answer 1

if sin x = sin a , then the general solution will be

x=nπ+
(-1)
a , where n$\epsilon$​​​​​​Z

Now , the equation given is :

2Sinx=√2

or , Sin x = √2/2 = 1/√2

or , Sin x=Sin π/4

therefore, the general solution is:

x=nπ+
(-1)
π/4 , where n$\epsilon Z$ .....eqn(1)

now , between 0 and 2π ie [0,2π] we have to find the values:

In eqn(1) , n=0 => x= π/4

n=1 => x= π-π/4 =3π/4

n=2 => x=2π+$(-1)^2$π/4

=2π+π/4 , which exceeds the value of 2π , so it's not accepted.

so the final solutiona are : x=π/4 and x=3π/4 (Answer)