Solve the following equations :
3 tan x + cot x = 5 cosec 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,
3tan x + cot x = 5cosec x
⇒
⇒
⇒
⇒
⇒ {∵ sin2 x + cos2 x = 1}
∴
⇒ = 0
⇒
⇒
⇒
∴ cos x = -3 (neglected as cos x lies between -1 and 1)
or cos x = � (accepted value)
∴
If cos x = cos y, implies x = 2nπ ± y, where n ∈ Z.
∴