## anonymous 3 years ago Tell me what i'm doing wrong, picture is attached.

1. anonymous

2. anonymous

3rd to 4th line - the numerator shows s^3 but a c appeared

3. anonymous

You also made a mistake on the RHS. You can't cross out the sin's and cos's like that.

4. anonymous

Instead there is a trig identity there.

5. anonymous

how do i fix this ? :S

6. anonymous

There is a trig identity on the RHS.

7. anonymous

At the 4th line, try combining the denominator

8. anonymous

|dw:1353385333795:dw|

9. anonymous

Doesnt the denominator get cancelled out already ?

10. anonymous

@Dido525 like this |dw:1353385466311:dw|

11. anonymous

|dw:1353385495522:dw|

12. anonymous

|dw:1353385573816:dw|

13. anonymous

Yeah that's right.

14. anonymous

For the left hand side, from the 3rd line, combine the denominator Then, factor the numerator This will allow you to use a trig identity to prove the original equation

15. anonymous

16. anonymous

it's okay, but is that way correct now ?

17. anonymous

yes its right

18. anonymous

Yes that is correct.

19. anonymous

@Skaematik like this |dw:1353385871631:dw|

20. anonymous

no

21. anonymous

$\frac{ s ^{4}+c ^{4}+2s ^{2}c ^{2} }{ cs }$

22. anonymous

i'm having difficulties seeing how it get's the fourth power, can you please explain

23. anonymous

@burhan101 : TO be honest I would only change ONE side to try and make it equal to the other not manipulate both.

24. anonymous

$\frac{ s ^{2}s }{ c } + \frac{ c ^{2}c }{ s } + 2s$

25. anonymous

Make the denominator cs Multiply 1st term by s Multiply 2nd term by c Multiply 3rd term by cs

26. anonymous

@dido525 changing the RHS is perfectly OK, in most cases it is actually the only way you can solve the problem without spending 234098723094 hours trying to go through ridiculous transformations

27. anonymous

Meh.

28. anonymous

@Dido525 yes, that's what my teacher want's us to try to do too, but im having alot of problems with this question, seems very complicated -.-

29. anonymous

Ohh!!! Hold on I am getting close!

30. anonymous

Okay :)

31. anonymous

Got it!!!!!

32. anonymous

And I only changed one side :) .

33. anonymous

Okay. The idea is we want to start with the complicated side. Lets choose the left side.

34. anonymous

Okay?

35. anonymous

okay !

36. anonymous

should we start fresh, from the given problem ?

37. anonymous

yes :) .

38. anonymous

Alrightt !

39. anonymous

So we have: |dw:1353386616775:dw|

40. anonymous

You know:|dw:1353386673693:dw|

41. anonymous

yup

42. anonymous

I would change the sin^2(x) and cos^2(x) To match that formula :) .

43. anonymous

Ohhh okay !

44. anonymous

Tell me what you get.

45. anonymous

|dw:1353386849843:dw| DO we change that into a one, or no ?

46. anonymous

i think i'm wrong -_-

47. anonymous

No you do not change that to a one.

48. anonymous

okay so first we change everything to sin & cos

49. anonymous

Well if sin^2(x) + cos^(x) =1 that what is Sin^2(x) equal to?

50. anonymous

No no!!!

51. anonymous

We want to keep tan and cot.

52. anonymous

why? that's how im taught to do it haha :\$

53. anonymous

it would be equal to 1/2

54. anonymous

But since we have a tan and cot on the other side it's natural we want to keep it that way :P . I was taught that way too ^_^ . Sometiems we gotta break the rules.

55. anonymous

ohhh alright, i see what you're saying

56. anonymous

So what do you get? Feel free to do it on paper and take pics.

57. anonymous

burhan, don't listen to him. You CAN change the right hand side (cot and tan). And sometimes you must. It makes no sense not to change them

58. anonymous

@Skaematik : But his teacher wants him to only change one side.

59. anonymous

It only took 4 steps lol @Skaematik .

60. anonymous

61. anonymous

No....

62. anonymous

@Skaematik i know i can but the thing is i have to do it my teacher's method or she takes off marks :(

63. anonymous

@Dido525 oh no :(

64. anonymous

sorry, im SO confused tho

65. anonymous

|dw:1353387439718:dw|

66. anonymous

:) .

67. anonymous

I am SURE you can do the rest :) .

68. anonymous

Expand it out and change the Tan(x) and Cot(x) into Sin's and cos's .

69. anonymous

okay, i will try

70. anonymous

|dw:1353387756754:dw|

71. anonymous

multiply those like that ?

72. anonymous

Yep!

73. anonymous

like that :S

74. anonymous

Good but leave sin(x)/cos(x) as Tan(x) and the cos(x)/sin(x) as Cot(x) .

75. anonymous

i can't i get marks taken off if i do, my teacher has a checklist that we MUST follow or she takes off marks :P

76. anonymous

okay, i don't know what to do from here on

77. anonymous

I would riot at the teacher TBH.

78. anonymous

Okay then.

79. anonymous

haha trust me me too :P

80. anonymous

We can cancel out a cos(x) from the first fraction and a sin(x) from the other fraction. You notice that?

81. anonymous

You have very neat handwriting Btw.

82. anonymous

Thank-you :)

83. anonymous

Like so :

84. anonymous

You Cannot do this!!!

85. anonymous

ohh

86. anonymous

|dw:1353388449271:dw| No!!!

87. anonymous

then what do i cancel out . :S

88. anonymous

You can only cancel out terms if they have the same common denominator. You do not have the same common denominator in this case :) .

89. anonymous

oh yeah, wooops

90. anonymous

|dw:1353388530585:dw|

91. anonymous

I KNOW you can solve the rest!

92. anonymous

does it look like this,

93. anonymous

Yep!

94. anonymous

DO YOU NOTICE SOMETHING YOU CAN CANCEL?!?!!?!

95. anonymous

So rry... I am a bit of a math freak lol.

96. anonymous

i'm afraid not :(

97. anonymous

Look harder!!! We have a 2Sin(x)scos(x) . We can eliminate that!!! We

98. anonymous

Do you see how?!?!?!

99. anonymous

sin^2x ?

100. anonymous

No!!!

101. anonymous

OH i think i see it

102. anonymous

-sinxcosx+2sinxcosx= sinxcosx

103. anonymous

VERY CLOSE!!!! We can get rid of that too!!!

104. anonymous

ohh i see it again haha |dw:1353389264088:dw|

105. anonymous

Yep!!!

106. anonymous

Yaaay ! :D

107. anonymous

So now we have: |dw:1353389317704:dw|

108. anonymous

one ?

109. anonymous

no

110. anonymous

|dw:1353389480538:dw|

111. anonymous

You know sin(x)/cos(x) is tan (x) :P .

112. anonymous

yuppp & cosx/sinx = cot

113. anonymous

GOod!

114. anonymous

|dw:1353389561044:dw|

115. anonymous

Hence proved :) .

116. anonymous

THANKYOU ! i swear only you had the patience to help me for so long ^.^ :)

117. anonymous

I remember I helped someone for 2 hour slol.

118. anonymous

thanksss again :D i would give you a cookie if i could haha

119. anonymous

I swear if the teacher takes marks off you need to protest. All of this is valid.

120. anonymous

I don't think she will because i changed the format to accommodate how she likes to mark !