- #1
Maria
Can someone please walk me trough this one:
cos2x = 2 cosx sinx :uhh:
cos2x = 2 cosx sinx :uhh:
I would have gotten to that eventually..mathwonk said:you might use the fact that 2cos(x)sin(x) = sin(2x) to transform the equation into something easier.
To solve for cos2x = 2 cosx sinx, you can use the double angle formula for cosine: cos2x = cos^2x - sin^2x. Then, substitute 2 cosx sinx for cos2x to get the equation 2 cosx sinx = cos^2x - sin^2x. From there, you can use algebraic manipulations to solve for x.
The double angle formula for cosine is cos2x = cos^2x - sin^2x.
Yes, you can use a calculator to solve for cos2x = 2 cosx sinx. However, it is important to note that calculators may not always give exact solutions, so it is important to double check your answer using algebraic manipulations.
Yes, there are other ways to solve for cos2x = 2 cosx sinx. One method is to use the half angle formula for cosine: cos2x = 2 cos^2(x/2) - 1. Another method is to use the Pythagorean identity: cos^2x + sin^2x = 1. By rearranging this identity, you can also solve for cos2x = 2 cosx sinx.
Yes, this equation can be solved for any value of x. However, it is important to note that there may be multiple solutions or no solutions at all, depending on the values of cosx and sinx. It is important to carefully consider the domain and range of the trigonometric functions when solving for x.