Question

write tan theta in terms of cosec theta​

Answer 1

Answer:

tan θ =1/√(cosec²θ - 1)

Step-by-step explanation:

we have to write tan θ in terms of cosec θ

we know that tan θ = 1/cotθ

also cosec²θ = cot²θ + 1

cot²θ = cosec²θ - 1

cot θ = √(cosec²θ - 1)

tan θ = 1/cotθ = 1/√(cosec²θ - 1)

tanθ   in terms of cosec θ   is

tan θ =1/√(cosec²θ - 1)

Answer 2

Answer:

tanθ  in terms of cosec θ   is

tan θ =1/√(cosec²θ - 1)

Step-by-step explanation:

• In context to the given , we have to find tan θ in terms of cosec θ
• Solution:

⇒ tan θ =1/√(cosec²θ - 1)

⇒ We have to write tan θ in terms of cosec θ

⇒ So, we have to find the relation between  tan θ and cosec θ

⇒ we know that;

tan θ = 1/cotθ [ eq. 1]

we have to find the relation between;

cotθ and cosecθ

we know that, [cosec²θ = cot²θ + 1 ]

cot²θ = cosec²θ - 1

cot θ = √(cosec²θ - 1)

By putting this value of cotθ in eq. 1

tan θ = 1/√(cosec²θ - 1)

Therefore, tanθ  in terms of cosec θ   is

tan θ =1/√(cosec²θ - 1)