Question

If cosec theta = 2, cot theta = root3 p then find p.​

Answer 1

Given, cosec theta = 2 & cot theta = √3p.

We know that, cosec 30° = 2.

Hence, theta = 30°.

cot theta = √3p

or, cot 30° = √3p

or, √3 = √3p

or, p = √3/√3

or, p = 1

Answer:

The value of p is 1.

Answer 2

$\LARGE{\color{coral}{\textsf{\textbf{ αnѕwєr }}}}$

We have,cosec θ = 2

cot θ = 3√p

Now, we know that,

$\rm \: {cosec}^{2} θ − {cot}^{2} θ = 1 \\ \\ \rm \dashrightarrow \: {2}^{2} − {(3√p)}^{2} = 1 \\ \\ \rm \dashrightarrow4 − {3p}^{2} = 1 \\ \\ \rm \dashrightarrow 4 − 1 = {3p}^{2} \\ \\ \rm \dashrightarrow {3p}^{2} = 3 \\ \\ \rm \dashrightarrow {p}^{2} = 1 \\ \\ \rm \dashrightarrow \red{ p = ±1}$