Question

Simplify cos x tan x – sin x cos^2 x.

a) cos(x)⋅(tan(x)−sin(x)⋅cos(x))
b)cos(x)⋅sin(x)
c)cos(x)⋅tan(x)
d) sin(x)

Answer 1

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.