Simplify the following expression to a single trigonometric term sin(360-x)*tan(-x)/cos(180 x)*(sin^2A cos^2A)

Still a typo. Is that 180+x or 180-x?

180x makes no sense.

And where do the A's fit in?

To simplify the given expression, let's break it down step by step:

Expression: sin(360 - x) * tan(-x) / cos(180x) * (sin^2A * cos^2A)

Step 1: Simplify sin(360 - x)

To simplify sin(360 - x), we can use a trigonometric identity: sin(360 - θ) = sin(θ). So, we have:

sin(360 - x) = sin(x)

Expression becomes: sin(x) * tan(-x) / cos(180x) * (sin^2A * cos^2A)

Step 2: Simplify tan(-x)

To simplify tan(-x), we can use the trigonometric identity: tan(-θ) = -tan(θ). So, we have:

tan(-x) = -tan(x)

Expression becomes: sin(x) * (-tan(x)) / cos(180x) * (sin^2A * cos^2A)

Step 3: Simplify cos(180x)

To simplify cos(180x), let's use another trigonometric identity: cos(180 - θ) = -cos(θ). In this case, we have:

cos(180x) = -cos(x)

Expression becomes: sin(x) * (-tan(x)) / (-cos(x)) * (sin^2A * cos^2A)

Step 4: Simplify (sin^2A * cos^2A)

Since (sin^2A * cos^2A) is already a product of trigonometric terms, we don't need to simplify it further.

Final expression: sin(x) * (-tan(x)) / (-cos(x)) * (sin^2A * cos^2A)

Now, the expression is simplified to a single trigonometric term.