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...