Question

To solve the equation 5sin(2x)=3cosx, you should rewrite it as___.​

Answer 1

A. cosx(10sinx-3)=0

Explanation:

5(2sinxcosx)=3cosx

10sinxcosx-3cosx=0

cosx(10sinx-3)=0

Answer 2

A

Explanation:

We want to solve the equation:

`5\sin(2x)=3\cos(x)`

To do so, we can rewrite the equation.

Recall the double-angle identity for sine:

`\sin(2x)=2\sin(x)\cos(x)`

By substitution:

`5\left(2\sin(x)\cos(x)\right)=3\cos(x)`

Distribute:

`10\sin(x)\cos(x)=3\cos(x)`

We can subtract 3cos(x) from both sides:

`10\sin(x)\cos(x)-3\cos(x)=0`

And factor:

`\cos(x)\left(10\sin(x)-3\right)=0`

Hence, our answer is A.

*It is important to note that we should not divide both sides by cos(x) to acquire 10sin(x) = 3. This is because we need to find the values of x, and one or more may result in cos(x) = 0 and we cannot divide by 0. Hence, we should subtract and then factor.