Question

2sin x • cosx = √3:2

Answer 1

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Answer 2

To solve the equation 2sin(x) • cos(x) = √3/2, we can use trigonometric identities. One of the most useful identities in this case is the double-angle identity for sine:

sin(2x) = 2sin(x) • cos(x).

Let's rewrite the given equation using this identity:

2sin(x) • cos(x) = √3/2.

sin(2x) = √3/2.

Now, we want to find the values of x that satisfy sin(2x) = √3/2.

We know that sin(π/3) = √3/2, so:

2x = π/3.

Now, to find all the solutions for x, we'll consider the general solutions of sin(2x) = √3/2. Since sin is a periodic function with a period of 2π, we can add any multiple of π to our solution.

The general solution for 2x = π/3 is:

2x = π/3 + 2πk,

where k is an integer (positive, negative, or zero). Now, solve for x:

x = (π/3 + 2πk)/2,

x = π/6 + πk.

So the solutions for x are:

x = π/6 + πk,

where k is an integer. These solutions cover all possible values of x that satisfy the given equation.