Question

Simplify the trig expression. Sin x tan x +cos x.

Answer 1

Question:

Simplify the trig expression. sin x tan x +cos x.

Solution:

Let the following trigonometric expression:

$\sin (x)\tan (x)\text{ + cos(x)}$

Rewriting using trigonometric identities:

$=\text{ }cos(x)\text{ +}\frac{\sin(x)}{\cos(x)}\sin (x)$

this is equivalent to:

$=\text{ }cos(x)\text{ +}\frac{\sin ^2(x)}{\cos (x)}$

Converting cos (x) to a fraction, this is equivalent to:

$=\text{ }\frac{\cos (x)\cos (x)}{\cos (x)}\text{+}\frac{\sin^2(x)}{\cos(x)}$

Since the denominators are the same, we can combine the fractions:

$=\text{ }\frac{\cos (x)\cos (x)+sin^2(x)}{\cos (x)}$

this is equivalent to:

$=\text{ }\frac{\cos ^2(x)+sin^2(x)}{\cos (x)}$

this is equivalent to:

$=\text{ }\frac{1}{\cos (x)}=\text{ }sec(x)$

then, we can conclude that the correct answer is :

$\sin (x)\tan (x)\text{ + cos(x) = sec(x)}$