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- Suppose a 3rd order constant coefficient ODE has a characteristic equation that had 3 distinct roots, equal to -2, 1 and 4. What is the general solution for this ODE?One, Two, Three (a) Show that tan(tan-1 1 + tan-1 2 + tan-1 3) = 0. (b) Conclude from part (a) that tan-1 1 + tan-1 2 + tan-1 3 = π Source: College Mathematics Journal, Vol. 37, No. 3, May 2006Verify. a. (2 tan x ) / (1 + tan2 x) = sin(2x) b. 1 / (1 − sin θ) + 1 / (1 + sin θ) = 2 sec2 θ c. 1 − (sin x − cos x)2 / (cos x) = 2 sin x
- suppose that cosx<=1 for all x>=0.Combine this with the first fundamental theorem of calculus to prove sinx<=x ,1-cosx<=x^2/2 for all x>=0.USe the same idea to prove x-sinx<=x^3/6 &x-x^3/6<=sinx<=x for all x>=0To prove cos (-u) csc (-u) tan (-u) = 1, which of the following is correct as a first step? a. cos (-u) csc (-u) tan (-u) = cos u (-csc u) (-tan u)b. cos (-u) csc (-u) tan (-u) = -cos u (csc u) (-tan u)c. cos (-u) csc (-u) tan (-u) =cos u (csc u) (tan u)d. cos (-u) csc (-u) tan (-u) = cos u (-csc u) (tan u)1. If tan x=1 then tan(−x)= 2. If sin x=0.2then sin(−x) = 3. If cos x=0.6 then cos(−x)= 4. If tan x=4 then tan(π+x)=