Use Rolle's Theorem to show that between any two roots of ( x-1)sinx=o there exists at least one of tanx=1-x

Answer 1

If y = (x-1) sinx, then
y' = sinx + (x-1)cosx = k sin(x+θ)
where cosθ = 1/√(1+(x-1)^2)
since k is never zero, the zeroes of y' are the same as the zeroes of y, just shifted by θ. That is, they are between the zeroes of y

Note that if
sinx + (x-1) cosx = 0
tanx + (x-1) = 0 (for cosx≠0)

Answer 2

Student

Answer 3

Batiru

Answer 4

Maths.Assignment

Answer 5

Use Rolle'Theorm to show that between any to roots of(x_1)since=0 there exist at least one roots of tanx=1_x