You are given 3  ropes and   a lighter.The  time required  to burn through rope 1  with a  single  flame is 20 minutes.Time required  to burn through rope 2  with   single  flame  is 30 minutes . Time required to burn rope 3 with a sinlge flame is 60 minutes.The burn rates  in differnet  sections in the  rope are  unknown  and vary. For how many integers M  in the  set{5,10,15,20...........100,105,110}is  it NOT possible to measure  out exactly M minutes  using the  3  ropes  and the  lighter?

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.