Solve the following equations :

sin x tan x – 1 = tan x – sin x

Ideas required to solve the problem:


The general solution of any trigonometric equation is given as –


• sin x = sin y, implies x = nπ + (– 1)ny, where n Z.


• cos x = cos y, implies x = 2nπ ± y, where n Z.


• tan x = tan y, implies x = nπ + y, where n Z.


given,


sin x tan x – 1 = tan x – sin x


sin x tan x – tan x + sin x – 1 = 0


tan x(sin x – 1) + (sin x – 1) = 0


(sin x – 1)(tan x + 1) = 0


sin x = 1 or tan x = -1


sin x = sin π/2 or tan x = tan (- π/4 )


If sin x = sin y, implies x = nπ + (– 1)ny, where n Z.


and tan x = tan y, implies x = nπ + y, where n Z.


x = nπ + (-1)n (π /2) or x = mπ + (- π/4)



7