## sabika13 3 years ago How do I solve this using trig identities: tan(pi/4 + x) +tan(pi/4 - x) =2sec2x

1. sabika13

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

2. nubeer

have you studied double angle identities?

3. sabika13

well i have the formulas for it

4. nubeer

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

5. sabika13

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

6. 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)

7. sabika13

and then do i conjugate?

8. 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.

9. 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.

10. sabika13

i ended up with tanx

11. sabika13

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

12. 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..

13. nubeer

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

14. sabika13

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

15. nubeer

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

16. sabika13

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

17. sabika13

right?

18. sabika13

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

19. sabika13

and then tanpi/4 =1

20. sabika13

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

21. sabika13

ru there?

22. nubeer

yes i am.. just solving for you..

23. nubeer

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

24. sabika13

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

25. sabika13

it will become a common deno

26. 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

27. nubeer

tell me if this helps you.