Question

if cot theta + cosec theta =l then find the value of tan theta in terms of l​

Answer 1

Answer:

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Answer 2

Concept:

Trigonometric ratios are the ratios of sides of the right-angle triangle.

Given:

cot Θ + cosec Θ = l

Find:

We are asked to find the value of (tan Θ) in terms of l​.

Solution:

We have,

cot Θ + cosec Θ = l

So,

Now,

Using Trigonometric Identities,

i.e.

cosec² Θ = cot² Θ + 1

⇒

cosec Θ = √(cot² Θ + 1 )

So,

Now,

Putting this value in the given equation,

i.e.

cot Θ + √(cot² Θ + 1 ) = l

Now,

√(cot² Θ + 1 ) = l - cot Θ

Now,

Squaring both sides,

[√(cot² Θ + 1 )]² = (l - cot Θ)²

Now, simplify,

(cot² Θ + 1 ) = l² + cot² Θ - 2 l cot Θ

⇒

-2 l cot Θ = 1 - l²

⇒

cot Θ = - [(1 - l²) / 2 l]

And,

We know that tan Θ is reciprocal of cot Θ,

So,

tan Θ = -[2 l / (1 - l²)]

Hence, the value of (tan Θ) in terms of l​ is  -[2 l / (1 - l²)].

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