Questions asked by Noel

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• How to prove #sin(theta+phi)/cos(theta-phi)=(tantheta+tanphi)/(1+tanthetatanphi)#?
  
• How to prove that #sin(A+B)sin(A-B)=sin^2A-sin^2B#?
  
• How to prove that #tan35+tan10+tan35tan10=1#?
  
• How to prove that #tan(pi/4+alpha)-tan(pi/4-alpha)=2tan2alpha#?
  
• How to prove that #2sin((4pi)/5)cos(pi/5)=sin((2pi)/5)#?
  
• How to prove that #cos^2((4pi)/7)-sin^2((3pi)/7)=cos((6pi)/7)#?
  
• Double Angle Formula Proving?
  
• How does #t^2-2t-1=0# become #t=1+-sqrt2#?
  
• Using #(1-cos2x)/(1+cos2x)=tan^2x#, how do you find the exact value of #tan(pi/8)#?
  
• Using #t=tan(1/2theta)#, how do you prove that #(tan2alpha+cotalpha)/(tan2alpha-tanalpha)=cot^2alpha#?
  
• Using #t=tan(theta/2)#, prove that #tan(x/2+pi/4)+tan(x/2-pi/4)=2tanx#?
  
• How to prove that #tan112 1/2=-sqrt2-1#?
  
• How to simplify #cos^2 2theta-sin^2 2theta#?
  
• How do you solve #2sin2xcos2x#?
  
• How do you simplify #sin4xcos4x#?
  
• How do you solve #sqrt3 tanalpha+1=0# if #alpha# is obtuse?
  
• How do you solve #cot^2theta=sqrt3 cottheta# in the domain #0<=theta<=360#?
  
• How do you solve #tan^2x+tanx=sqrt3 tanx + sqrt3# for the domain #0<=x<=360#?
  
• How do you solve #sqrt2 sin2theta+1=0#?
  
• How do you find the general solution of #sqrt2 sin2theta+1=0#?
  
• How do you prove that #tan(180-A)sin(270+A)cosec(360-A)=-1#?
  
• How do you solve #|x^2-1|<=3 and |x^2+1|>=0#, preferably by graphing?
  
• How do you solve #|x+2|+|x-2|=4#?
  
• How do you find #a# for the derivative of #f(x)=x^2-ax# if the tangent has a y-intercept of -9 at the vertex?
  
• A gas tank holds 3625L of butane at 850mmHg. What is the volume of the butane at 25°C?