Question

if tan(20-3alpha)=cot (5alpha-20) then find the value of alpha

Answer 1

Tan (20 - 3 α) = Cot (5 α - 20)

Sin (20 - 3α) * Sin (5 α -20) = Cos (5α - 20) Cos(20 - 3α)

Cos [ (5α - 20) + (20-3α) ] = 0

Cos 2 α =  π/2    or  3π/2 

α = π/4  or  3π/4

you can also find the general solution    as    2α = n π + π/4  or  n π - π/4