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{ +}(\sin(x))/(\cos(x))\sin (x)`

this is equivalent to:

`=\text{ }cos(x)\text{ +}(\sin ^2(x))/(\cos (x))`

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

`=\text{ }(\cos (x)\cos (x))/(\cos (x))\text{+}(\sin^2(x))/(\cos(x))`

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

`=\text{ }(\cos (x)\cos (x)+sin^2(x))/(\cos (x))`

this is equivalent to:

`=\text{ }(\cos ^2(x)+sin^2(x))/(\cos (x))`

this is equivalent to:

`=\text{ }(1)/(\cos (x))=\text{ }sec(x)`

then, we can conclude that the correct answer is :

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