maths qn.

• jay_rocks

  6 Feb 06, 13:29

  anyone noes how to do these qns?
  
  lg(2x+5) = 1 + lg x
  
  prove e identity : (1+ cosec teater) ( 1 - sin teater) = cos teater cot teater
  
  and
  
  (1 - sin A + cos A)² = 2(1-sin A) ( 1+ cos A)
  
  teater = 0 < --- like degree tt thing.
• ndmmxiaomayi

  6 Feb 06, 13:35

  Originally posted by jay_rocks:

  anyone noes how to do these qns?
  
  lg(2x+5) = 1 + lg x
  
  prove e identity : (1+ cosec teater) ( 1 - sin teater) = cos teater cot teater
  
  and
  
  (1 - sin A + cos A)² = 2(1-sin A) ( 1+ cos A)
  
  teater = 0 < --- like degree tt thing.

  Log question I don't know.
  
  Express cosec in terms of sin. Then work out.
  
  Last question: Expand the equation.
  _____________________________________________________________
  
  Working for last question (I think so, not sure correct or not, quite long never touch A Maths)
  
  (1 - sinA + cosA)^2 = (1 - sinA + cosA)(1 - sinA + cosA)
  = 1 - sinA + cosA - sinA + sin^2A - sinAcosA + cosA - sinAcosA + cos^2A
  
  Identity used (sin^2A + cos^2A = 1)
  = 1 + 1 - 2sinA + 2cosA - 2sinAcosA
  = 2 - 2sinA + 2cosA - 2sinAcosA
  = 2(1 - sinA)(1 + cosA)
• Icemoon

  6 Feb 06, 13:35

  Originally posted by jay_rocks:

  anyone noes how to do these qns?
  
  lg(2x+5) = 1 + lg x

  1 is lg10 right?
  
  then combine lg10 and lgx together.
  
  can solve liao right?
• jay_rocks

  6 Feb 06, 13:37

  Originally posted by Icemoon:

  1 is lg10 right?
  
  then combine lg10 and lgx together.
  
  can solve liao right?

  thx a lot. suddenly forgot what was 1 equals to
• sinicker

  6 Feb 06, 13:50

  teater or kiter or diter or....??
• jay_rocks

  6 Feb 06, 13:59

  Originally posted by sinicker:

  teater or kiter or diter or....??

  teater
• jay_rocks

  6 Feb 06, 13:59

  Originally posted by ndmmxiaomayi:

  Log question I don't know.
  
  Express cosec in terms of sin. Then work out.
  
  Last question: Expand the equation.
  _____________________________________________________________
  
  Working for last question (I think so, not sure correct or not, quite long never touch A Maths)
  
  (1 - sinA + cosA)^2 = (1 - sinA + cosA)(1 - sinA + cosA)
  = 1 - sinA + cosA - sinA + sin^2A - sinAcosA + cosA - sinAcosA + cos^2A
  
  Identity used (sin^2A + cos^2A = 1)
  = 1 + 1 - 2sinA + 2cosA - 2sinAcosA
  = 2 - 2sinA + 2cosA - 2sinAcosA
  = 2(1 - sinA)(1 + cosA)

  thx a lot.
• CoolMyth

  6 Feb 06, 14:01

  Originally posted by jay_rocks:

  anyone noes how to do these qns?
  
  lg(2x+5) = 1 + lg x
  
  prove e identity : (1+ cosec teater) ( 1 - sin teater) = cos teater cot teater
  
  and
  
  (1 - sin A + cos A)² = 2(1-sin A) ( 1+ cos A)
  
  teater = 0 < --- like degree tt thing.

  i)log (2x+5) = 1 + log x
  
  --> log (2x+5) - log x = 1
  
  --> log [(2x+5)/x] = 1
  
  --> (2x + 5)/x = 10, x not equal to zero.
  
  --> 2x + 5 = 10x
  
  --> 8x = 5
  
  --> x = 5/8
  
  ii) (1+ cosec x)(1 - sin x) = cos x cot x
  
  LHS
  = (1+ cosec x)(1 - sin x)
  = 1 - sin x + cosec x - 1
  = cosec x - sin x
  = (1 - sin^2 x)/sin x
  = cos^2 x/sin x
  = (cos x)(cos x/sin x)
  = cos x cot x
  = RHS
  
  iii)(1 - sin x + cos x)² = 2(1- sin x)(1+ cos x)
  
  LHS
  = (1 - sin x + cos x)²
  = (1 - sin x + cos x)(1 - sin x + cos x)
  = 1 - sin x + cos x - sin x - sin^2 x - sin x cos x + cos x - sin x cos x + cos^2 x
  = (1 - sin^2 x + cos^2 x) - 2 sin x + 2 cos x - 2 sin x cos x
  = 2 - 2 sin x + 2 cos x - 2 sin x cos x (Since (1 - sin^2 x + cos^2 x) = 2)
  = 2(1 + cos x - sin x - sin x cos x)
  = 2(1 - sin x)(1 + cos x)
  = RHS
  
  For any maths problem, please visit Virtual Maths Clinic!
• jay_rocks

  6 Feb 06, 14:08

  Originally posted by CoolMyth:
  
  
  ii) (1+ cosec x)(1 - sin x) = cos x cot x
  
  LHS
  = (1+ cosec x)(1 - sin x)
  = 1 - sin x + cosec x - 1
  = cosec x - sin x
  = (1 - sin^2 x)/sin x<---- [b] how come become like this??
  = cos^2 x/sin x
  = (cos x)(cos x/sin x)
  = cos x cot x
  = RHS
  
  [/b]

• CoolMyth

  6 Feb 06, 14:13

  cosec x = 1/sin x, correct?
  
  So,
  
  cosec x - sin x
  
  = (1/sin x) - sin x, correct?
  
  Just do like your usual (1/x) - x = (1 - x^2)/x
  
  So,
  
  (1/sin x) - sin x = (1 - sin^2 x)/sin x = cos^2 x/sin x
• papercut87

  6 Feb 06, 14:14

  because:
  
  cosec x - sin x
  = 1/sinx - sin²x/sinx
  = (1-sin²x)/sinx
  =cos²x/sinx
  =(cosx/sinx)(cosx)
  = cosx cotx (shown)
• jay_rocks

  6 Feb 06, 14:17

  ylrc. hate trigo sia..btw, thx a lot
• CoolMyth

  6 Feb 06, 14:19

  Originally posted by jay_rocks:

  ylrc. hate trigo sia..btw, thx a lot

  Got any more questions?
  
  Remember to visit Virtual Maths Clinic!
• jay_rocks

  6 Feb 06, 14:41

  Originally posted by CoolMyth:

  Got any more questions?
  
  Remember to visit Virtual Maths Clinic!

  ok. np.