Final answer:
The expression cos x tan x - sin x cos^2 x simplifies to cos(x)⋅(tan(x)−sin(x)⋅cos(x)).
Step-by-step explanation:
The expression cos x tan x - sin x cos^2 x can be simplified as cos(x)⋅(tan(x)−sin(x)⋅cos(x)). To simplify, we first distribute the cos x to both terms inside the parentheses. This gives us cos(x)⋅tan(x)−cos(x)⋅sin(x)⋅cos(x). Next, we can simplify further by factoring out a cos(x) from the second term. This gives us cos(x)⋅(tan(x)−sin(x)⋅cos(x)). Therefore, option a) cos(x)⋅(tan(x)−sin(x)⋅cos(x)) is the simplified form of the expression.