Verify the identity sec^2 x cot x - cot x = tan x

Question

lgbasallote · Answer

by verify you mean to prove right?

anonymous · Answer

yes

lgbasallote · Answer

well i'll go with the left hand side since it is more complicated..you'd like to do that part in proving..

so...factor out cotx first..

$$\large \mathbf{cotx(sec^2x - 1)}$$

do you know what to do next?

$\large \mathsf{\text{Hint:}}$ $\large \mathsf{tan^2x + 1 = sec^2x}$

anonymous · Answer

make sec^2x-1 tan^2x?

anonymous · Answer

not minus but exchange

anonymous · Answer

cotx(tan^2 x)

lgbasallote · Answer

right! now change to sines and cosines...

anonymous · Answer

i have (cos x/sin x)(1/cos^2 x)

lgbasallote · Answer

you got the cotx right...but tan^2 x is NOT 1/cos^2 x...try again

anonymous · Answer

woopsies sec^2x -1 is tan^2x

lgbasallote · Answer

no no..change tan^2 x in terms of sines and cosines..

anonymous · Answer

which is $$\sin ^{2} x/\cos ^{2} x$$

lgbasallote · Answer

right! so...

$\Huge (\frac{cos}{sin})(\frac{sin^{2}x}{cos^{2}x})$

what do you think comes next?

anonymous · Answer

factor

anonymous · Answer

noooo

anonymous · Answer

cancel out

anonymous · Answer

leaving only sin x/cos x

anonymous · Answer

which is tan x

lgbasallote · Answer

$$\Huge \checkmark$$

anonymous · Answer

yaaaaay

anonymous · Answer

thank you for making me try, that helped out instead of just telling me the answer!!

lgbasallote · Answer

well that is what all users of OpenStudy must do :DDD <tips hat>

anonymous · Answer

ok, on to solving trig equations dun dun dun

lgbasallote · Answer

$\large \mathsf{\text{Goodluck! Have Fun!}}$  :DDD

anonymous · Answer

:)

lgbasallote · Answer

...i would appreciate some medal for the hard work *whistles* lol haha =)) you should award people for their hard work yknow ;D

anonymous · Answer

i just started this website today!
I have no idea how to use it yet

anonymous · Answer

how do i give you a medal

anonymous · Answer

ill give you 1000

anonymous · Answer

lol

lgbasallote · Answer

ha thanks :D and by the way...


$\Huge \mathbb{\text{WELCOME TO OPENSTUDY!!!}}$

remember to give medals to those you think gave you the best answer/explanation ;D

lgbasallote · Answer

^hope you can rad that..coz it got cut in mine

lgbasallote · Answer

read*

anonymous · Answer

i love it! but how do you give medals? by clicking best answer?

lgbasallote · Answer

yepp :DD

lgbasallote · Answer

you might wanna check this site http://openstudy.com/study#/groups/OpenStudy%20Feedback read some of the posts of the users with the violet names (they're the site moderators) you can learn about the current functions in OpenStudy from those posts :DD

anonymous · Answer

i wish i knew about open study a year ago

lgbasallote · Answer

haha lol yeah..this is a great site to learn ^_^