Question

Solve the following equations :

cosec x = 1 + cot 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, 

cosec x = 1 + cot x

⇒ sin x + cos x = 1

In all such problems we try to reduce the equation in an equation involving single trigonometric expression.

NOTE: We can also make the ratio of sin instead of cos , the answer remains same but the form of answer may look different, when you put values of n you will get same values with both forms 

If cos x = cos y, impls x = 2nπ ± y, where n∈ Z