Question

cosec theta + cot theta no spam plz ​

Answer 1

Answer:

cosec θ = 1/sin θ

cot θ = 1/tan θ = 1/(sin θ /cos θ ) = cos θ /sin θ

So,

cosec θ - cot θ

= 1/sin θ - cos θ /sin θ

= (1-cos θ )/sin θ

cosec θ - cot θ = (1-cos θ )/sin θ

Again,

Multiplying with sin θ in the numerator and denominator of the RHS,

cosec θ - cot θ

= [sin θ (1 - cos θ)]/sin^2 θ

= [sin θ (1 - cos θ)]/(1 - cos^2 θ)

= [sin θ (1 - cos θ)]/[(1 + cos θ)(1 - cos θ)]

= sin θ /(1 + cos θ)

Hence,

cosec θ - cot θ = (1-cos θ )/sin θ = sin θ /(1 + cos θ)