Question

If cosec theta=4 and cot theta=√3k the value of k

Answer 1

Answer :-

Value of k is 5 or - 5.

Explanation :-

Given :-

• cosec θ = 4

• cot θ = √3 k

To find :-

Value of k

Solution :-

We know that

cosec² θ - cot² θ = 1

By substituting the given values

⇒ (4)² - (√3 k)² = 1

⇒ 16 - 3k² = 1

⇒ 16 - 1 = 3k²

⇒ 15 = 3k²

⇒ 15/3 = k²

⇒ 5 = k²

⇒ ± √5 = k

⇒ k = ± √5

⇒ k = + 5 or - 5

∴ the value of k is 5 or - 5.

Answer 2

SOLUTION:-

Given:

⚫cosec theta=4

⚫cot theta= √3k

Therefore,

$cot \theta = \sqrt{3k} \\ \\ = > {cot}^{2} \theta = 3k \\ \\ = > cosec {}^{2} \theta - 1 = 3k \: \: \: \: \: \: \: \: \: [1 + {cot}^{2} \theta = {cosec}^{2} \theta]\\ \\ = > {4}^{2} - 1 = 3k \: \: \: \: \: \: \: [substituting \: cosec \theta = 4 \: ] \\ \\ = > 16 - 1 = 3k \\ \\ = > 15 = 3k \\ \\ = > k = \frac{15}{3} \\ \\ = > k = 5$

Thus,

The value of k is 5.

Hope it helps ☺️