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While determining the number of solutions the equation can have , we use these formulas .   General solutions to some of the standard equations Equation Solution Sin θ Θ  = nπ , n ∈  Z Cos θ Θ  = (2n+1) π /2  ,  n ∈  Z Tan θ  = 0 Θ  = n π  , n ∈  Z Sin θ  = 1 Θ  = (4n+1) π /2  ,  n ∈  Z Sin θ  = -1 Θ  = (4n-1) π /2  ,  n ∈  Z Cos θ  = 1 Θ  = 2nπ , n ∈  Z Cos θ  = -1 Θ  = (2n+1 )π, n ∈  Z Cot θ  = 0 Θ  = (2n+1 ) π /2 ,  n ∈  Z   EQUATIONS OF ANOTHER TYPES           1.    When the equation is of the form sin θ = sin α             General solution to the equation is given by θ = n π + (-1) n , n ∈ Z       2.    When the equation is of the form cos θ =  cos α   ...

To prove that   lim x⟶0  [sinx/x]=0 , where [.] denotes greatest integer function . We must first prove that sin x/x tends to 1 from the values that are  less than 1 as x tends to zero PROOF : Now as x tends to zero, x can take any of the values tending from right of zero and   tending from left side of zero  Case - 1:                  First we assume that x tends from   right of the zero               Now,  If x= 0.001,   sin(0.001)/0.001     = 0.999999833                         If x=0.0001,  sin(0.0001/0.0001) = 0.999999998   Case -2:                 Now we assume that x is tending from left of the zero                  If   x= -0.001,      sin(-0.00...