Find sin 2x, cos 2x, and tan 2x from the given information.
cos x = 15/17
csc x < 0

The trigonometry values are:, and

The given parameter is:

If csc(x) is less than 0, then sin(x) is less than 0.

Using the following trigonometry ratio,

Substitute

Expand

Collect like terms

Take LCM

Take square roots

Recall that, the sine of the angles is negative.

So, we have:

sin(2x) is then calculated as:

This gives

cos(2x) is then calculated as:

This gives

Take LCM

Lastly, tan(2x) is calculated using:

So, we have:

Read more about trigonometry ratios at:

link

Step-by-step explanation: