Question

If tan Ɵ=4 and cot Ɵ= √3 k, then k=

(a) 1 (b) 2

(c)√5 (d) 5​

Answer 1

Answer:

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Answer 2

SOLUTION:-

Given:

⚫cosec theta=4

⚫cot theta= √3k

$Therefore,</p><p>\begin{gathered}cot \theta = \sqrt{3k} \\ \\ = > {cot}^{2} \theta = 3k \\ \\ = > cosec {}^{2} \theta - 1 = 3k \: \: \: \: \: \: \: \: \: [1 + {cot}^{2} \theta = {cosec}^{2} \theta]\\ \\ = > {4}^{2} - 1 = 3k \: \: \: \: \: \: \: [substituting \: cosec \theta = 4 \: ] \\ \\ = > 16 - 1 = 3k \\ \\ = > 15 = 3k \\ \\ = > k = \frac{15}{3} \\ \\ = > k = 5 \end{gathered}$

Thus,

The value of k is 5.

Hope it helps ☺️