Question

PLEASE HELP Use basic identities to simplify the expression

1/ (cot^2 θ )+ sec θ cos θ

Answer 1

sec^2θ

Answer 2

i believe...

Answer 3

Well, since I'm from Europe, I'll convert everything to tan, sin and cos functions ;)
\[\frac{ 1 }{ \cot^2 \theta }+\sec \theta \cos \theta =\tan^2 \theta +\frac{ 1 }{ \cos \theta }\cos \theta=\tan^2 \theta + 1\]Looks good enough for me!

Answer 4

1/cot = tan
sec/cos = 1

tan^2 + 1 = sec^2

so your answer i believe is

Answer 5

Thank you! can you help me with another question real quick? :)

Answer 6

Just quickly ask it!

Answer 7

Simplify the expression.
(cos^2 x+ sin^2 x)/(cot^2x -csc^2 x)

Answer 8

You MUST know a real simple answer to cos²x+sin²x!

Answer 9

While you are thinking about that one, I'll give cot^2x -csc^2 x a try...

Answer 10

The entire thing can be solved by knowing:

sin^2+cos^2=1

divide the whole thing by cos^2

cot^2+1=csc^2

Answer 11

\[\cot^2x -\csc^2 x=\frac{ \cos^2 x }{ \sin^2 x }-\frac{ 1 }{ \sin^2 x }=\frac{ \cos^2x - 1 }{ \sin^2 x }\] is what I have so far...
Now that looks promising!
I really need to now the answer of cos²x+sin²x now!

Answer 12

cos²x+sin²x equals 1

Answer 13

Now divide both sides of the equation by sin^2(x). You'll see you can plug in entire equations for the top and bottom.

Answer 14

OK, thanks @Kainui, I'm sure @haleyw knew that!
So: we've got \[\frac{ 1 }{ \frac{ \cos^2 x -1 }{ \sin^2 x } }\]

Answer 15

No, you don't know it either, that's why I'm telling you.

Answer 16

(cos^2 x+ sin^2 x)/(cot^2x -csc^2 x)

cos^2 x+ sin^2 x=1
divide this by sin^2(x)
cot^2x+1=csc^2x
subtract 1 and csc^2(x) from either side
cot^2x-csc^2x=-1

Plug them both into the original equation
(1)/(-1)

Answer 17

Just turn upside down:\[\frac{ \sin^2 x }{ \cos^2 -1 }=-\frac{ \sin^2 x }{ 1- \cos^2 x }=-\frac{ \sin^2 x }{ \sin^2 x }=-1\]

Answer 18

Thank you both so much! I really appreciate it!

Answer 19

In this last step, I used if cos²x + sin²x=1, then sin²x = 1 - cos²x.
I only had cos²x - 1, so I reversed them and put a minus sign in front of the fraction.

Answer 20

It seems to be customary to express your appreciation by pressing the "Best Response" buttons...;)

Answer 21

Glad to be of help!

Answer 22

:)