if 9cosx+12sinx=15
find the value of cotx

• 9cosx + 12sinx = 15
  => 3cosx + 4sinx = 5
  dividing by cosx
  => 3 + 4tanx = 5secx
  squaring
  => 9 + 16tan^2x + 24tanx = 25sec^2x = 25(1 + tan^2x)
  => 9tan^2x - 24tanx + 16 = 0
  => (3tanx - 4)^2 = 0
  => 3tanx - 4 = 0
  => tanx = 4/3
  => cotx = 3/4
  
• 10 years agoHelpfull: Yes(5) No(0)
• 9cosx+12sinx=15
  3cosx+4sinx=5
  divided by sinx
  3(cosx/sinx)+4(sinx/sinx)=5/sinx
  3cotx+4=5+5cotx because {cosecx=(1+cotx)}
  -2cotx=1
  cotx=-(1/2)
• 10 years agoHelpfull: Yes(0) No(1)
• 9cosx+12sinx=15
  
  => 3cosx+4sinx=5
  
  => 3cotx+4 = 5cosecx (on dividing both sides by sinx)
  squaring
  => 9cot^2x + 16 + 24cotx = 25cosec^2x
  => 9cot^2x + 16 + 24cotx = 25 + 25cot^2x
  => 16cot^2x - 24cotx + 9 = 0
  => cotx = 24/32
  => cotx = 3/4
• 10 years agoHelpfull: Yes(0) No(0)
• 9cosx + 12sinx=15
  => 3cosx+4 sinx=5
  => 3/5cosx+4/5sinx=1
  hence,
  also we know that from identities law
  cotx=cosx/sinx
  cotx=3/5/4/5
  = 3/4
  
  
• 9 years agoHelpfull: Yes(0) No(0)