Question

If cosec θ+ cot θ=5/2,then the value of tan 0 is​

Answer 1

Step-by-step explanation:

Given:-

Cosec θ + Cot θ = 5/2

To find:-

Find the value of Tan θ ?

Solution:-

Given that

Cosec θ + Cot θ = 5/2--------(1)

We know that

Cosec^2 θ - Cot^2 θ = 1

It is in the form of a^2-b^2

Where a = Cosec θ and b = Cot θ

We know that

(a+b)(a-b)=a^2-b^2

=> Cosec^2 θ - Cot^2 θ = 1

=> (Cosec θ+ Cot θ)(Cosec θ- Cot θ) = 1

=> (5/2)(Cosec θ - Cot θ) = 1

=> Cosec θ - Cot θ = 1/(5/2)

Cosec θ - Cot θ = 2/5 --------(2)

On subtracting (2) from (1)

Cosec θ + Cot θ = 5/2

Cosec θ - Cot θ = 2/5

(-) (+) (-)

_____________________

0 + 2 Cot θ = (5/2)-(2/5)

_____________________

=> 2 Cot θ = (5/2)-(2/5)

=> 2 Cot θ = (25-4)/10

=> 2 Cot θ = 21/10

=> Cot θ = (21/10)/2

=> Cot θ = 21/(10×2)

=> Cot θ = 21/20

We know that

Cot A = 1/Tan A

=> 1/ Tan θ = 21/20

=> Tan θ = 20/21

Answer:-

The value of Tan θ for the given problem is 20/21

Used formulae:-

• (a+b)(a-b)=a^2-b^2

• Cosec^2 θ - Cot^2 θ = 1

• Cot A = 1/Tan A