simplify cos(360-x)tanx/ sin(x-180)cos(90+x)
start with
cos(360-x) = cosx
sin(x-180) = -sinx
cos(90+x) = -sinx
and see where that takes you
To simplify the expression cos(360-x)tan(x)/sin(x-180)cos(90+x), let's break it down step by step:
1. Start with cos(360-x). Since the cosine function has a periodicity of 360 degrees, cos(360-x) is the same as cos(-x).
2. Next, simplify tan(x)/sin(x-180). The tangent function can be written as sin(x) / cos(x), so we have sin(x)/(sin(x-180)*cos(x)).
3. Now, simplify cos(90+x). The cosine function has a periodicity of 360 degrees, so cos(90+x) is the same as cos(90+x-360), which simplifies to cos(x-270).
Putting it all together, the simplified expression becomes:
cos(-x) * sin(x) / (sin(x-180) * cos(x) * cos(x-270))
Further simplification can be done by canceling out common factors and rearranging the terms, if necessary.