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
![](https://www.sarthaks.com/?qa=blob&qa_blobid=808852867190167128)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=10226005884213512242)
∴ cos x = -3 (neglected as cos x lies between -1 and 1)
or cos x = 1/2 (accepted value)
∴ cos x = cos \(\frac{π}3\)
If cos x = cos y, implies x = 2nπ ± y, where n ∈ Z.
∴ x = 2nπ ± \(\frac{π}3\) where n ∈ Z....ans