## burhan101 2 years ago Solve without a calculator

1. burhan101

$\[\huge 4\tan^2-\sec^2x=0$\]

2. burhan101

0<x<2pi

3. burhan101

@UnkleRhaukus

4. UnkleRhaukus

$4\tan^2 (x)-\sec^2 (x)=0$

5. burhan101

yup

6. UnkleRhaukus

$\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}$$\sec(\theta)=\frac{1}{\cos(\theta)}$

7. UnkleRhaukus

•take the sec term to the other side of the equation, •substitute the above definitions into your equation, •multiply by the denominator •divide by 4 •take the sqrt of both sides , •take the inverse trig function to isolate x

8. UnkleRhaukus

tell me if you get stuck.

9. burhan101

$4\frac{ \sin^2x }{ \cos^2x }-\frac{ 1 }{ \cos^2x }=0$

10. burhan101

what do i do next

11. UnkleRhaukus

multiply by cos^2

12. burhan101

to subtract the two ??

13. burhan101

(2sinx+1)(2sinx-1) / cos^2x

14. UnkleRhaukus

how did that happen?

15. burhan101

idk im guessing :S

16. UnkleRhaukus

start again and follow the •'s

17. burhan101

okay

18. burhan101

i'm going to be honest, im confused

19. burhan101

by following the checlist this is what im getting sinxcosx-sinx

20. Hero

May I suggest another approach?

21. UnkleRhaukus

...

22. burhan101

my teacher has a completely different way im confuseeed

23. UnkleRhaukus

well im sure there are many different ways ,

24. burhan101

25. Yahoo!

1 + tan^2 x = sec^2 x tan^2 x = sec^2 x - 1

26. UnkleRhaukus

i dont like that way as much as i like the way i have outlined , but that is opinion

27. Yahoo!

4 ( sec^2 x - 1) - sec^2 x = 0 4 sec^2 x - 4 - sec^2 x = 0 3 sec^2 x = 4 sec x = 2/ sqrt (3)

28. burhan101

i am only allowed to have cos and sin in my answers

29. Yahoo!

Lol.....u shuld have Mentioned that in the question...)

30. burhan101

Steps: 1. rearrange and isolate the unknown 2. move everything to one since, set equal to zero 3. use the zero principle 4. use inverse trig to find the angle 5. use CAST or ASTC to adjust answers @Yahoo! i know sorry ! :\$

31. Hero

|dw:1355392376220:dw|

32. burhan101

guys I GOT IT ! :D

33. burhan101

i just used my teachers method but everyone's explanations helped. thankyou :D

34. Hero

And what exactly was your teacher's method?

35. burhan101

we're supposed to find what x can and cannot equal

36. burhan101

so i just used basic trig and then looking at the unit circle i did elimination and listed the factors

37. Hero

That's not what you posted at the beginning

38. burhan101

burhan101 0 Steps: 1. rearrange and isolate the unknown 2. move everything to one since, set equal to zero 3. use the zero principle 4. use inverse trig to find the angle 5. use CAST or ASTC to adjust answers

39. burhan101

thats what i did, using the zero principle :

40. Hero

You mind showing some of those steps using the drawing button like I did?

41. burhan101

|dw:1355393054138:dw|

42. Hero

43. UnkleRhaukus

$4\tan^2 (x)-\sec^2 (x)=0$$4\tan^2 (x)=\sec^2 (x)$$4\left(\frac{\sin(x)}{\cos (x)}\right)^2 =\left(\frac1{\cos(x)}\right)^2$$4\frac{\sin^2(x)}{\cos^2 (x)} =\left(\frac1{\cos^2(x)}\right)$$4\sin^2(x)=\frac{\cos^2(x)}{\cos^2(x)}$$4\sin^2(x) =1$$\sin^2(x) =\frac14$$\sin(x)=\frac 12$$x=\arcsin\left(\frac12\right)=60°$

44. Hero

@UnkleRhaukus, you ignore negative values?

45. UsukiDoll

wow Hero that's just harsh, but...yeah..no comment

46. UsukiDoll

I'm not saying it sucks or anything though

47. RolyPoly

$4\tan^2 (x)-\sec^2 (x)=0$$4\tan^2 (x)-(1+tan^2x)=0$$3\tan^2 (x)-1=0$$tan^2x = \frac{1}{3}$That shouldn't be difficult.

48. RolyPoly

Just use the identity $$1+tan^2x=sec^2x$$

49. UnkleRhaukus

@hero 0<x<2pi stated in question

50. Hero

I didn't see that second line. He posted it in pieces.