Question

if sin theta =1/2 then the value of (tan theta + cot theta)^2 is

Answer 1

Step-by-step explanation:

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Answer 2

The value of the expression is 16/3

Step-by-step explanation:

Given that

$\sin\theta=\frac{1}{2}$

The relation between cosine and sine function is

$\cos\theta=\sqrt{1-\sin^2\theta}\\\\\cos\theta=\sqrt{1-(\frac{1}{2})^2}\\\\\cos\theta=\sqrt{1-\frac{1}{4}}\\\\\cos\theta=\frac{\sqrt{3}}{2}$

Now find the value of tan and cot

$\tan\theta=\frac{\\sin\theta}{\cos\theta}\\\\\tan\theta=\frac{1/2}{\sqrt3/2}\\\\\tan\theta=\frac{1}{\sqrt3}$

And

$\cot\theta=\frac{1}{\tan\theta}\\\\\cot\theta=\frac{1}{1/\sqrt3}\\\\\cot\theta=\sqrt3$

Substituting these values in the given expression

$(\tan\theta+\cot\theta)^2\\\\=(\frac{1}{\sqrt3}+\sqrt3)^2\\\\=(\frac{4}{\sqrt3}+3)^2\\\\=\frac{16}{3}$

#Learn More:

If cosec theta =3/2. Find the value of 2(cosec2 theta + cot2 theta)

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