can someone help with verifying a trig function?

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can someone help with verifying a trig function?

Mathematics
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try us? lols won't know till you post the question
\[(\sin \theta-\cos \theta)^{2}=1-2\sin^{2} \theta \cot \theta , Verify?\]
i'm going to skip the theta sign so here goes sin^2 - 2sin*cos + cos^2 = 1 - 2sin^2(cos/sin) sin^2 - cos^2 = 1 1 - 2 sin*cos = 1 - 2sin(cos they are equal make sense?

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thank you but just give me a second to make sure i got it
sure thing
how did you get to sin^2 - 2sin*cos + cos^2 = 1 - 2sin^2(cos/sin)
where did the 2sin come from specifically
i foiled the left side of the equation and tangent is equal to sin/cos so cot is equal to cos/sin
(a - b)^2 a^2 -2ab + b^2 it's foil
does that make sense?
i think im having trouble with the foiling
umm do you know how to foil? (a - b)(a - b) a^2 - ab - ab + b^2 (sin - cos)(sin - cos) sin^2 - sin*cos - sin*cos + cos^2 sin^2 - 2sin*cos + cos^2
okay thank you for yor help i see what i was doing wrong, i was foiling wrong, little rusty on the algebra
no problem
hey you have time for another?
sure
Sec^4-tan^4, what trig function is it equal to?
sec is 1/cos
1/cos^4 - sin^4/ cos^4 (1 - sin^4) / cos^4 cos^2 + sin^2 = 1 so cos^2 = 1 - sin^2 [(1 - sin^2)(1 + sin^2)]/ cos^4 (1 + sin^2)/ cos^2
i'm not sure if you can get more simplified than that..
sin^2 = 1 - cos^2 (1 + 1 - cos^2)/ cos^2 (2 - cos^2) / cos^2 2sec^2 - 1 there that's one trig function
the choices are A) Sec^2 B) csc C) tan D) Sec^2+tan^2 E) sin^2 F) sin*tan
the answer is D where i stopped first (1 + sin^2)/ cos^2 if you divide that out you'll get sec^2 + tan^2
ohh man thanks that one was killin me lol just for my own knowledge where do you start first when you see a problem like that? like what goes through your mind first?
i hate doing trig functions all i can say is something that you've probably heard 100s of times practice but seriously, the more you practice, the easier it is key hints cos^2 + sin^2 = 1 <-- super big and useful tan = sin/cos there are also the rarer ones half angle formulas
just move the functions around until you see something familiar and you'll see things to cancel out your object to make it as simple as possible
ok cool keep those in mind i have one question, how did you go from [(1 - sin^2)(1 + sin^2)]/ cos^4 to (1 + sin^2)/ cos^2
i wrote before that line that cos^2 = 1 - sin^2 which i got from sin^2 + cos^2 = 1 see? very useful since those are equal, i canceled from top and bottom does that make sense?
yes i see it now, and i see how you were left with the answer. your helping me out big time lol
lol awesome ^_^
alright ive got another one for you ive been trying it for a while but keep hittin dead ends, got time?
go for it
1/2(1+sin/cos+cos/1+sin) , what trig function is equal? Sin cos tan csc sec cot
cos/1? you sure, caz that's just cos
yup cos/(1+sin)
oh i see you need to use parenthesis rocco, otherwise there's a lot of miss understandings
ohh im sorry
oh and the first part is (1+sin)/cos
1/2(1+tan+cos+cot))
T-T
i feel quite useless....
give me some time, i'm going to write this out, sorry
no problem, and ure not useless dont worry about that lol
rocco i have no luck for this one :x sorry! repost this one
ok no prob, found another one, wanna take a crack at it, i thnk i got half of it?
rofl sure
ok its csc - cot = 1/ (csc + cot) verify
(csc - cot)(csc + cot) = 1 csc^2 - cot^2 = 1 ^-- that's another rule you should remember
ohh but can you cross the = sign when verifying?
i'm not sure i understand what you mean?
somewhere i heard that when you verify the = becomes like a wall that you cant cross and only work on either side to make them equal, maybe im just understanding your work wrong
i don't think i've heard that rule 2 + 4 = 8 - 2 if i add 2 on to both sides (crossing?) i get 6 = 6 do you mean crossing like this?
yea like that
it's perfectly fine as i just shown up there LOL 6 is equal to 6 so it's fine cheers ^_^
ohh i see, haha thanks youve been a big help!!!

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