## Yahoo! 3 years ago Find the general solution of tan2x = -cot(x+pie/3)?

1. A.Avinash_Goutham

u kno tan2x = 2tanx/1-tan^2x nd cotx = 1/tanx

2. A.Avinash_Goutham

form a quadratic nd solve........ for tanx........ then u l get the g.s

3. waterineyes

$\tan(2x) = -\cot(90 + x -30) \implies -(-\tan(x-30)) = \tan(x - \frac{\pi}{6})$ $\implies \tan(2x) = \tan(x - \frac{\pi}{3})$

4. waterineyes

General solution is given by: $\tan ( \theta) = \tan(x)$ then: $\theta = n \pi + x$

5. waterineyes

so: $2x = n \pi + ( x - \frac{\pi}{3} ) \implies x = n \pi + \frac{\pi}{3}$

6. Yahoo!

hey @waterineyes but my books says it as x = n pie + 5pie/6

7. waterineyes

So put n = 0 1 2 3 4 etc etc and find the corresponding value of x..

8. waterineyes

you can subtract it from $$2 \pi$$..

9. Yahoo!

wat???

10. waterineyes

Wait something got wrong.. Let me check..

11. Yahoo!

@w\ r uthere

12. waterineyes

Wait I am checking it..

13. waterineyes

I got it..

14. sauravshakya

|dw:1343210793286:dw|

15. waterineyes

$\tan(2x) = \cot(-x-60) \implies \cot(90 - (x + 150)) \implies \tan(x + 150)$ $\tan(2x) = \tan(x + 150)$

16. waterineyes

150 is in degrees: $150^{\circ} = \frac{5 \pi}{6}$

17. waterineyes

So: $2x = n \pi + x + \frac{5 \pi}{6}$

18. Yahoo!

wat the wrong in 1 st method!!

19. waterineyes

and subtract x from both sides: $x = n \pi + \frac{5 \pi}{6}$

20. waterineyes

21. Yahoo!

thxxx

22. waterineyes

Welcome dear..