anonymous
  • anonymous
sinx cscx -cscx+2sinx=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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apoorvk
  • apoorvk
sinx cscx = 1 therefore, 1- (1/sinx)+ 2sinx=0 so, [2(sinx)^2 + sinx -1]sinx =0. we can eliminate sinx in denominator but as sinx can be zero, and then equation will then become infinity. so basically we will write a pre-note that x is unequal to any n(pi), where n is an integer. next in the the equation we substitute sinx with any variable 't' and solve like any quadratic, then the solutions of sinx will come 2t^2 +t -1 = 0 we get t= sinx = 1/2 or -1. so x can be pi/6 or -pi/2 in th eprinciple values, or 2n(pi) added to the prinicipal values for a general set of solutions.
anonymous
  • anonymous
thank you. can please help me with this problem sin 3x cos x - cos 3x sin x=.5
apoorvk
  • apoorvk
okay easy. (sin a) (cos b) + (cos a) (sin b) = sin(a+b) so here th eaboce equation gets down to sin(3x+x)= 0.5 sin inverse of half = 4x so 4x = 30 degrees so x = 7.5 degrees.

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anonymous
  • anonymous
tanx cotx -tanx + 2cotx= 0
apoorvk
  • apoorvk
try this one now its similar to the first one that you asked!! in fact exactly the same procedure!
anonymous
  • anonymous
sin 3x cos x - cos 3x sin x=.5 you gave me the answer to positive cos 3x not negative
apoorvk
  • apoorvk
oops sorry. my bad. then the formula condenses to sin(A-B) as you may have gusesed so, sin(3x-x) = sin2x = 0.5 2x= 30 degrees so x= 15 degrees.

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