How do I solve this using trig identities: tan(pi/4 + x) +tan(pi/4 - x) =2sec2x

Question

anonymous · Answer

i tried left side: 1+tanx+1-tanx
=2 :S

nubeer · Answer

have you studied double angle identities?

anonymous · Answer

well i have the formulas for it

nubeer · Answer

ok good tell me formula for tan(a+b) and tan (a-b)
remember a and b are angles.

anonymous · Answer

tan(a+/-b)=(tana+/-tanb)/(1+/-tanatanb)

nubeer · Answer

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 · Answer

and then do i conjugate?

nubeer · Answer

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 · Answer

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 · Answer

i ended up with tanx

anonymous · Answer

actually it was 1+tan^2x/1+tanx

nubeer · Answer

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 · Answer

hmm i dont think so you did right.. as far as i know there should be 
1-tan^2x in the denominator.

anonymous · Answer

i got (1+tanx)(1-tanx)in deno

nubeer · Answer

yes.. multiplying it would give (1-tan^2x)

anonymous · Answer

okaylet me show what i did:
tanpi/4 + tanx)^2/(1-tanpi/4tanx)(1+tanpi/4tanx) + tanpi/4-tanx/1+tanpi/4+tanx

anonymous · Answer

right?

anonymous · Answer

(tanpi/4+tanx)^2 + (tanpi/4-tanx) / (1-tanpi/4tanx)(1+tanpi/4tanx)

anonymous · Answer

and then tanpi/4 =1

anonymous · Answer

2+tan^2x-tanx / 1-tan^2x

anonymous · Answer

ru there?

nubeer · Answer

yes i am.. just solving for you..

nubeer · Answer

ok well fault i found in your answer is in frist step.
tanpi/4 + tanx)^2 how you got the square here?

anonymous · Answer

i multiplied (tan pi/4 +tanx) to both top and bottom

anonymous · Answer

it will become a common deno

nubeer · Answer

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 · Answer

tell me if this helps you.