anonymous
  • anonymous
How do I solve this using trig identities: tan(pi/4 + x) +tan(pi/4 - x) =2sec2x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
i tried left side: 1+tanx+1-tanx =2 :S
nubeer
  • nubeer
have you studied double angle identities?
anonymous
  • anonymous
well i have the formulas for it

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nubeer
  • nubeer
ok good tell me formula for tan(a+b) and tan (a-b) remember a and b are angles.
anonymous
  • anonymous
tan(a+/-b)=(tana+/-tanb)/(1+/-tanatanb)
nubeer
  • nubeer
good.. now try to use this formula in your question.. it would be some thing like this for tan(pi/4 +x) = [tan(pi/4) +tanx]/(1-tan(pi/4)tanx)
anonymous
  • anonymous
and then do i conjugate?
nubeer
  • nubeer
yes.. basically tan(pi/4) = 1 so just start solving as pi/4 will be eliminated.. the rest would be LCM and simple algebra.
nubeer
  • nubeer
i think it should work.. as where 2 angles are involved we use double angle identities to make stuff easy for us.. so this should work out.
anonymous
  • anonymous
i ended up with tanx
anonymous
  • anonymous
actually it was 1+tan^2x/1+tanx
nubeer
  • nubeer
seriously.. hmm i will solve it and will see.. i have to go right now but will be back in a while just post the working u did.. if i can do i will post back..
nubeer
  • nubeer
hmm i dont think so you did right.. as far as i know there should be 1-tan^2x in the denominator.
anonymous
  • anonymous
i got (1+tanx)(1-tanx)in deno
nubeer
  • nubeer
yes.. multiplying it would give (1-tan^2x)
anonymous
  • anonymous
okaylet me show what i did: tanpi/4 + tanx)^2/(1-tanpi/4tanx)(1+tanpi/4tanx) + tanpi/4-tanx/1+tanpi/4+tanx
anonymous
  • anonymous
right?
anonymous
  • anonymous
(tanpi/4+tanx)^2 + (tanpi/4-tanx) / (1-tanpi/4tanx)(1+tanpi/4tanx)
anonymous
  • anonymous
and then tanpi/4 =1
anonymous
  • anonymous
2+tan^2x-tanx / 1-tan^2x
anonymous
  • anonymous
ru there?
nubeer
  • nubeer
yes i am.. just solving for you..
nubeer
  • nubeer
ok well fault i found in your answer is in frist step. tanpi/4 + tanx)^2 how you got the square here?
anonymous
  • anonymous
i multiplied (tan pi/4 +tanx) to both top and bottom
anonymous
  • anonymous
it will become a common deno
nubeer
  • nubeer
ok i got easy way.. try wolfram.. http://www.wolframalpha.com/input/?i=tan%28pi%2F4+%2B+x%29+%2Btan%28pi%2F4+-+x%29+%3D2sec%282x%29&dataset=&equal=Submit
nubeer
  • nubeer
tell me if this helps you.

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