anonymous
  • anonymous
can someone help with verifying a trig function?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
try us? lols won't know till you post the question
anonymous
  • anonymous
\[(\sin \theta-\cos \theta)^{2}=1-2\sin^{2} \theta \cot \theta , Verify?\]
anonymous
  • anonymous
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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anonymous
  • anonymous
thank you but just give me a second to make sure i got it
anonymous
  • anonymous
sure thing
anonymous
  • anonymous
how did you get to sin^2 - 2sin*cos + cos^2 = 1 - 2sin^2(cos/sin)
anonymous
  • anonymous
where did the 2sin come from specifically
anonymous
  • anonymous
i foiled the left side of the equation and tangent is equal to sin/cos so cot is equal to cos/sin
anonymous
  • anonymous
(a - b)^2 a^2 -2ab + b^2 it's foil
anonymous
  • anonymous
does that make sense?
anonymous
  • anonymous
i think im having trouble with the foiling
anonymous
  • anonymous
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
anonymous
  • anonymous
okay thank you for yor help i see what i was doing wrong, i was foiling wrong, little rusty on the algebra
anonymous
  • anonymous
no problem
anonymous
  • anonymous
hey you have time for another?
anonymous
  • anonymous
sure
anonymous
  • anonymous
Sec^4-tan^4, what trig function is it equal to?
anonymous
  • anonymous
sec is 1/cos
anonymous
  • anonymous
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
anonymous
  • anonymous
i'm not sure if you can get more simplified than that..
anonymous
  • anonymous
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
anonymous
  • anonymous
the choices are A) Sec^2 B) csc C) tan D) Sec^2+tan^2 E) sin^2 F) sin*tan
anonymous
  • anonymous
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
anonymous
  • anonymous
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?
anonymous
  • anonymous
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
anonymous
  • anonymous
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
anonymous
  • anonymous
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
anonymous
  • anonymous
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?
anonymous
  • anonymous
yes i see it now, and i see how you were left with the answer. your helping me out big time lol
anonymous
  • anonymous
lol awesome ^_^
anonymous
  • anonymous
alright ive got another one for you ive been trying it for a while but keep hittin dead ends, got time?
anonymous
  • anonymous
go for it
anonymous
  • anonymous
1/2(1+sin/cos+cos/1+sin) , what trig function is equal? Sin cos tan csc sec cot
anonymous
  • anonymous
cos/1? you sure, caz that's just cos
anonymous
  • anonymous
yup cos/(1+sin)
anonymous
  • anonymous
oh i see you need to use parenthesis rocco, otherwise there's a lot of miss understandings
anonymous
  • anonymous
ohh im sorry
anonymous
  • anonymous
oh and the first part is (1+sin)/cos
anonymous
  • anonymous
1/2(1+tan+cos+cot))
anonymous
  • anonymous
T-T
anonymous
  • anonymous
i feel quite useless....
anonymous
  • anonymous
give me some time, i'm going to write this out, sorry
anonymous
  • anonymous
no problem, and ure not useless dont worry about that lol
anonymous
  • anonymous
rocco i have no luck for this one :x sorry! repost this one
anonymous
  • anonymous
ok no prob, found another one, wanna take a crack at it, i thnk i got half of it?
anonymous
  • anonymous
rofl sure
anonymous
  • anonymous
ok its csc - cot = 1/ (csc + cot) verify
anonymous
  • anonymous
(csc - cot)(csc + cot) = 1 csc^2 - cot^2 = 1 ^-- that's another rule you should remember
anonymous
  • anonymous
ohh but can you cross the = sign when verifying?
anonymous
  • anonymous
i'm not sure i understand what you mean?
anonymous
  • anonymous
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
anonymous
  • anonymous
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?
anonymous
  • anonymous
yea like that
anonymous
  • anonymous
it's perfectly fine as i just shown up there LOL 6 is equal to 6 so it's fine cheers ^_^
anonymous
  • anonymous
ohh i see, haha thanks youve been a big help!!!

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