Solve the following equations :
Ideas required to solve the problem:
The general solution of any trigonometric equation is given as –
• sin x = sin y, implies x = nπ + (– 1)n y, 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,
⇒
⇒
⇒
∴ tan x = -1 or tan x = √3
As, tan x ϵ (-∞ , ∞) so both values are valid and acceptable.
⇒ tan x = tan (-π/4) or tan x = tan (π/3)
If tan x = tan y, implies x = nπ + y, where n ∈ Z.
Clearly by comparing standard form with obtained equation we have
y = -π/4 or y = π/3
∴ or
Hence,
,where m,n ϵ Z