Question

Show that the equation tan 2x = 5 sin 2x can be written in the form (1 - 5 cos 2x) sin 2x = 0

Answer 1

To show that the equation tan 2x = 5 sin 2x can be written in the form (1 - 5 cos 2x) sin 2x = 0, we can start by using the trigonometric identity tan 2x = sin 2x / cos 2x.

Step-by-step explanation:

To show that the equation tan 2x = 5 sin 2x can be written in the form (1 - 5 cos 2x) sin 2x = 0, we can start by using the trigonometric identity tan 2x = sin 2x / cos 2x. Substitute this into the original equation:

sin 2x / cos 2x = 5 sin 2x

Next, multiply both sides by cos 2x:

sin 2x = 5 sin 2x cos 2x

Now, we can rearrange the equation:

5 sin 2x cos 2x - sin 2x = 0

Factoring out sin 2x, we get:

sin 2x (5 cos 2x - 1) = 0

Finally, we have the equation in the desired form (1 - 5 cos 2x) sin 2x = 0.