Trigonometric EquationsGeneral Solutions1. tan x = 2P. 2nπ±2π3,n∈I2. sin x = √32Q. nπ−π4,n∈I3. cos x =−12R. nπ+(−1)nπ3,n∈I4. cot x = -1S. nπ+tan−1(2),n∈I
1 - S, 2 - R, 3 - P, 4 - Q
The expression involving an integer 'n' which gives all solutions of a trigonometric equation is called general solution.
1. tan x = 2
tan x = tan {tan−1 (2) }
General solution when tan x = tan α
x = nπ + α
So general solution is x = nπ + tan−1 (2) n ∈ I
2. sin x = √32
sin x = sin π3
x = nπ + (−1)n π3 n ∈ I
3. cos x = - 12
cos x = cos 2π3
x = 2nπ ± 2π3 n ∈ I
4. cot x = -1
cot x = cot(- π4)
x = nπ - π4 n ∈ I