Q. 2 G5.0( 1 Vote )
Find the general solutions of the following equations :
tan 2x tan x = 1
Answer :
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,
⇒ 
⇒ 
We know that: cot θ = tan (π/2 – θ)
∴ 
If tan x = tan y, then x is given by x = nπ + y, where n ∈ Z.
From above expression, on comparison with standard equation we have
y = 
∴ 
⇒ 
⇒ 
,where n ϵ Z ….ans
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