Question

If cosec theta+ cot theta = 5, then evaluate sec theta.​

Answer 1

Answer:

13/12

Step-by-step explanation:

Cosecθ + Cotθ = 5

1 + Cosθ = 5Sinθ

(1 + Cosθ)² = (5Sinθ)²

(1 + Cosθ)² = 25Sin²θ

(1 + Cosθ)² = 25 (1 - Cosθ)²

(1 + Cosθ)² = 25 (1 - Cosθ)(1 + Cosθ)

1 + Cosθ = 25 ( 1 - Cosθ)

1 + Cosθ = 25 - 25Cosθ

26Cosθ = 24.

Cosθ = 24/ 26 = 12/13.

Secθ = 13/12

Answer 2

Step-by-step explanation:

cosecθ+cotθ=5

➡(1+cosθ)/sinθ=5

➡1+cosθ=5sinθ

➡(1+cosθ)²=25sin²θ

➡(1+cosθ)²=25(1-cos²θ)

➡(1+cosθ)²=25(1+cosθ)(1-cosθ)

➡1+cosθ=25(1-cosθ)

➡1+cosθ=25-25cosθ

➡26cosθ=24

➡cosθ=24/26=12/13

➡secθ=13/12