Question

Can someone check my answer?
Simplify the expression
cos x + sin x tan x
My answer: sec x

Answer 1

That's correct.

Answer 2

Thanx!

Answer 3

It was kind of a guess, so can you please explain how to get that answer?

Answer 4

@mathmale @mathstudent55
Please HELP

Answer 5

@SolomonZelman

Answer 6

Sure. Here's how I would do it (there are multiple methods I'm sure):

First: Convert tan(x) to sin and cos\[\cos(x)+\sin(x)(\frac{ \sin(x) }{ \cos(x) })\] Now multiply the sin(x) \[\cos(x)+\frac{ \sin ^{2}(x) }{ \cos(x) }\] Then find a common denominator \[\cos(x)(\frac{ \cos(x) }{ \cos(x) })+\frac{ \sin ^{2}(x) }{ \cos(x) }\] Multiply the cos(x) and make it all one fraction\[\frac{ \cos ^{2}(x)+\sin ^{2}(x) }{ \cos(x) }\] Now by Trig identities you know that\[\sin ^{2}(x)+\cos ^{2}(x)=1\] So it becomes \[\frac{ 1 }{ \cos(x) }=\sec(x)\]

Answer 7

Wow, thank you sooo much.
Now I get it.

Answer 8

You're welcome, I'm glad I could help :)