Question

simplify the trigonometric expression
*problem below*

Answer 1

\[ \frac{ \sin x }{ \cos x }+\frac{ \cos x }{ \sin x}\]

Answer 2

just add the fractions.

Answer 3

That's like adding\[{x \over y} + {y\over x}\]

Answer 4

\[ {\sin^2 x + \cos^2 x \over\sin x \cos x} \]

Answer 5

Note that the numerator is 1.

Answer 6

when i worked it out on a web calculator it gave me the answer tan(x) + cos(x) but i knew it was wrong because the answer was multiple choice

Answer 7

my only choices are
a. (sec x)(csc x)
b. 1
c 2(sin x)(cos x)/sin^2x + cos^2x

Answer 8

Since\[2\sin(x)\cos(x) = {\sin(2x)}\]we may say\[\sin(x)\cos(x) = 0.5\sin(2x)\]

Answer 9

We already have,\[{1 \over 0.5\sin(2x)} \implies 2\sin(2x) \implies 4\sin(x)\cos(x)\]

Answer 10

but which one of those answers does that come out to. im not sure how to get from that to one of my choices

Answer 11

@ParthKohli - you showed the first step correctly, i.e.:\[\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}={\sin^2 x + \cos^2 x \over\sin x \cos x}=\frac{1}{\sin x\cos x}\]

Answer 12

I found a mistake.

Answer 13

the next step is to notice that:\[\frac{1}{\sin x}=cosec x\]and:\[\frac{1}{\cos x}=sec x\]

Answer 14

yes. those are the only options given with the question being "which of the following is the correct simplification of the trigonometric expression?"

Answer 15

I made a very elementary mistake...

Answer 16

Ironically, I was doing the SAME question earlier this day and I did it correctly!

Answer 17

:)

Answer 18

lol. its ok we all make mistakes sometimes.

Answer 19

@kizzfan911 you should now be able to work out the correct answer from the information given to you.

Answer 20

ok. ill see what i can do.

Answer 21

hint:\[\frac{1}{\sin x\cos x}=\frac{1}{\sin x}\times\frac{1}{\cos x}\]

Answer 22

i ended up getting sec(x)/sin(x)

Answer 23

use the two clues I gave above regarding what 1/sin x equals, and what 1/cos x equals

Answer 24

cosec(x) is the same as csc(x)

Answer 25

0h ok. so its (sec x)(csc x)? i was entering it into the calculator wrong

Answer 26

yes :)

Answer 27

thank you. your help is much appreciated.

Answer 28

yw :)