Evaluate the following expression.(x ≠ π/2+πn,where n is a whole number)
2 cos x + 2 sin x tan x

A)-2 sec x
B)2 sec x
C)4 cos x
D)-4 cos x
E)3 sin x

Question

Evaluate the following expression.(x ≠ π/2+πn,where n is a whole number) ​
2 cos x + 2 sin x tan x
​
A)-2 sec x
B)2 sec x
C)4 cos x
D)-4 cos x
E)3 sin x

Quizplus · Accepted Answer

The expression can be simplified as follows: $2 \cos x + 2 \sin x \tan x$. Since $\tan x = \frac{\sin x}{\cos x}$, the expression becomes $2 \cos x + 2 \sin x \cdot \frac{\sin x}{\cos x}$. This simplifies to $2 \cos x + 2 \frac{\sin^2 x}{\cos x}$. Using the Pythagorean identity, $\sin^2 x = 1 - \cos^2 x$, we can rewrite the expression as $2 \cos x + 2 \frac{1 - \cos^2 x}{\cos x}$. This simplifies further to $2 \cos x + 2 \frac{1}{\cos x} - 2 \cos x$, where $2 \cos x$ and $-2 \cos x$ cancel out, leaving $2 \frac{1}{\cos x}$, which is $2 \sec x$.

Evaluate the Following Expression