Question

Verify sec x(csc x − 2 sin x) = cot x − tan x ?

Answer 1

What is sec= to?

Answer 2

1/cos?

Answer 3

Yup! Now try distributing that into the parenthesis

Answer 4

sec x(csc x − 2 sin x) = 1/cosx (1/sinx - 2sin^2 x/?)

Answer 5

That's a terrible way to do it -_-

But it works...Just look at that first unknown box...what do you think goes there? To make it match up with the left side

Answer 6

*Big hint there in the next step, you can see inside the parenthesis have been put over a common denominator*

Answer 7

sin(x) for the next two blanks?! Thank you!

Answer 8

Correct!

Answer 9

I'm confused how to get the third blank though

Answer 10

And the third box...they just multiplied in the 1/cos(x) into the parenthesis

So we know 1 * the numerator is just the numerator

But now that we know sin(x) is on the bottom...and that is being multiplied by cos(x)...what is our new denominator?

Answer 11

*Don't overthink it! :)

Answer 12

Is this an identity?
Sorry, I am really bad at these problems because we just started with this in our class

Answer 13

Nope, no identity

Haha reason why i said don't over think it :)

What is cos(x) * sin(x)? Literally just cos(x)sin(x)

That is your new denominator!

Answer 14

\[\sec x \left( \csc x-2\sin x \right)=\sec x \left( \frac{ 1 }{ \sin x }-2\sin x \right)\]
\[=\sec x \left( \frac{ 1-2\sin ^2x }{ \sin x } \right)=\frac{ \cos ^2x+\sin ^2x-2\sin ^2x }{ \cos x \sin x }\]
\[=\frac{ \cos ^2x-\sin ^2x }{ \cos x \sin x }=?\]

Answer 15

Lol yes as @sshayer has put above in a neater fashion :)

Answer 16

Oh wow! Lol okay thank you! So the 4th blank is the same?

Answer 17

So those 3,4 and 5 boxes should be easy for you to fill in

Answer 18

Indeed boxes 3 and 4 are the same

Answer 19

Box 5 is quite simple as well...

Answer 20

Got it! Thank you so much! I am so glad I found out about this website! Is it free all the time or is there like a trial first?

Answer 21

Free all the time!

There was a system in place before where you could pay to get "Qualified helper assistance" but that has sense disappeared *For the moment*

But yeah, it's a great resource for help!

Answer 22

^Ignore my bad grammar there XD *sense --> Since*

Answer 23

Awesome! Thanks again!!)