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.



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