Simplify the following expression to a single trigonometric term sin(360-x)*tan(-x)/cos(180 x)*(sin^2A cos^2A) answer= -sinx*-tanx/cosx*(1) after that how do i continue?
sin(360-x) = -sin(x)
tan(-x) = -tan(x)
cos(180-x) = -cos(x)
so, you have
sin(x)tan(x)/cos(x) = sin^2(x)/cos^2(x) = tan^2(x)
Not sure where the A comes from, but you get the idea. Just reduce everything to simple trig functions and then combine them. If you need further help, please fix all the typos and get back to us.
To continue simplifying the expression, we can simplify the given expression:
-sin(x) * (-tan(x)) / cos(x) * 1
Since the negative signs in the numerator and denominator cancel each other out, we have:
sin(x) * tan(x) / cos(x) * 1
Using the identity tan(x) = sin(x) / cos(x), we can rewrite the expression as:
sin(x) * sin(x) / cos(x) * 1
Simplifying further, we have:
sin^2(x) / cos(x) * 1
Since sin^2(x) = 1 - cos^2(x), we can substitute this into the expression:
(1 - cos^2(x)) / cos(x) * 1
Now you can continue simplifying, if desired.
To simplify the expression -sin(x) * -tan(x) / cos(x) * (1):
1. Multiply -sin(x) and -tan(x) together:
sin(x) * tan(x) / cos(x) * (1)
2. Divide by cos(x):
sin(x) * tan(x) / cos^2(x) * (1)
3. Since tan(x) = sin(x) / cos(x), we can replace tan(x) in the expression:
sin(x) * (sin(x)/cos(x)) / cos^2(x) * (1)
4. Combine the fractions:
sin(x) * sin(x) / (cos(x) * cos^2(x)) * (1)
5. Simplify cos^2(x) to (cos(x))^2:
sin(x) * sin(x) / (cos(x) * (cos(x))^2) * (1)
6. Simplify (cos(x))^2 to cos^2(x):
sin(x) * sin(x) / (cos(x) * cos^2(x)) * (1)
7. Simplify the numerator, sin(x) * sin(x), to (sin(x))^2:
(sin(x))^2 / (cos(x) * cos^2(x)) * (1)
8. Simplify cos(x) * cos^2(x) to cos^3(x):
(sin(x))^2 / cos^3(x) * (1)
So, the simplified expression is: (sin(x))^2 / cos^3(x)