Q. 2 I

Find the general solutions of the following equations :

tan px = cot qx

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


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