## burhan101 2 years ago Tell me what i'm doing wrong, picture is attached.

1. burhan101

2. Skaematik

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

3. Dido525

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

4. Dido525

Instead there is a trig identity there.

5. burhan101

how do i fix this ? :S

6. Dido525

There is a trig identity on the RHS.

7. Skaematik

At the 4th line, try combining the denominator

8. Dido525

|dw:1353385333795:dw|

9. burhan101

Doesnt the denominator get cancelled out already ?

10. burhan101

@Dido525 like this |dw:1353385466311:dw|

11. Dido525

|dw:1353385495522:dw|

12. burhan101

|dw:1353385573816:dw|

13. Dido525

Yeah that's right.

14. Skaematik

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. Dido525

16. burhan101

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

17. Skaematik

yes its right

18. Dido525

Yes that is correct.

19. burhan101

@Skaematik like this |dw:1353385871631:dw|

20. Skaematik

no

21. Skaematik

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

22. burhan101

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

23. Dido525

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

24. Skaematik

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

25. Skaematik

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

26. Skaematik

@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. Dido525

Meh.

28. burhan101

@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. Dido525

Ohh!!! Hold on I am getting close!

30. burhan101

Okay :)

31. Dido525

Got it!!!!!

32. Dido525

And I only changed one side :) .

33. Dido525

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

34. Dido525

Okay?

35. burhan101

okay !

36. burhan101

should we start fresh, from the given problem ?

37. Dido525

yes :) .

38. burhan101

Alrightt !

39. Dido525

So we have: |dw:1353386616775:dw|

40. Dido525

You know:|dw:1353386673693:dw|

41. burhan101

yup

42. Dido525

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

43. burhan101

Ohhh okay !

44. Dido525

Tell me what you get.

45. burhan101

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

46. burhan101

i think i'm wrong -_-

47. Dido525

No you do not change that to a one.

48. burhan101

okay so first we change everything to sin & cos

49. Dido525

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

50. Dido525

No no!!!

51. Dido525

We want to keep tan and cot.

52. burhan101

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

53. burhan101

it would be equal to 1/2

54. Dido525

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. burhan101

ohhh alright, i see what you're saying

56. Dido525

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

57. Skaematik

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. Dido525

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

59. Dido525

It only took 4 steps lol @Skaematik .

60. burhan101

61. Dido525

No....

62. burhan101

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

63. burhan101

@Dido525 oh no :(

64. burhan101

sorry, im SO confused tho

65. Dido525

|dw:1353387439718:dw|

66. Dido525

:) .

67. Dido525

I am SURE you can do the rest :) .

68. Dido525

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

69. burhan101

okay, i will try

70. burhan101

|dw:1353387756754:dw|

71. burhan101

multiply those like that ?

72. Dido525

Yep!

73. burhan101

like that :S

74. Dido525

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

75. burhan101

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. burhan101

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

77. Dido525

I would riot at the teacher TBH.

78. Dido525

Okay then.

79. burhan101

haha trust me me too :P

80. Dido525

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

81. Dido525

You have very neat handwriting Btw.

82. burhan101

Thank-you :)

83. burhan101

Like so :

84. Dido525

You Cannot do this!!!

85. burhan101

ohh

86. Dido525

|dw:1353388449271:dw| No!!!

87. burhan101

then what do i cancel out . :S

88. Dido525

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. burhan101

oh yeah, wooops

90. Dido525

|dw:1353388530585:dw|

91. Dido525

I KNOW you can solve the rest!

92. burhan101

does it look like this,

93. Dido525

Yep!

94. Dido525

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

95. Dido525

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

96. burhan101

i'm afraid not :(

97. Dido525

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

98. Dido525

Do you see how?!?!?!

99. burhan101

sin^2x ?

100. Dido525

No!!!

101. burhan101

OH i think i see it

102. burhan101

-sinxcosx+2sinxcosx= sinxcosx

103. Dido525

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

104. burhan101

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

105. Dido525

Yep!!!

106. burhan101

Yaaay ! :D

107. Dido525

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

108. burhan101

one ?

109. burhan101

no

110. burhan101

|dw:1353389480538:dw|

111. Dido525

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

112. burhan101

yuppp & cosx/sinx = cot

113. Dido525

GOod!

114. burhan101

|dw:1353389561044:dw|

115. Dido525

Hence proved :) .

116. burhan101

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

117. Dido525

I remember I helped someone for 2 hour slol.

118. burhan101

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

119. Dido525

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

120. burhan101

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

Find more explanations on OpenStudy