Question

Solve the following equations : 

3 tan x + cot x = 5 cosec x

Answer 1

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

∴ 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