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.