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,
⇒
⇒
⇒
∴ either, or
⇒ or
⇒ or
⇒ or
If tan x = tan y, implies x = nπ + y, where n ∈ Z.
Clearly by comparing standard form with obtained equation we have:
y = π/6 or y = -π/3
∴ or
Hence,
,where m,n ϵ Z