Question

If sin @ =1/2
then find the value of (tan 0 + coto)​

Answer 1

Answer:

jfngohxkhkhxkhxoxksoydodpufupdulduldlyd kgxhldjlchlc hdlhdhlcjl kgxjlck mhxtkulckskjdulfjl

Answer 2

The value of the expression is 16/3

Step-by-step explanation:

Given that

\sin\theta=\frac{1}{2}sinθ=

2

1

The relation between cosine and sine function is

\begin{gathered}\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}\end{gathered}

cosθ=

1−sin

2

θ

cosθ=

1−(

2

1

)

2

cosθ=

1−

4

1

cosθ=

2

3

Now find the value of tan and cot

\begin{gathered}\tan\theta=\frac{\\sin\theta}{\cos\theta}\\\\\tan\theta=\frac{1/2}{\sqrt3/2}\\\\\tan\theta=\frac{1}{\sqrt3}\end{gathered}

And

\begin{gathered}\cot\theta=\frac{1}{\tan\theta}\\\\\cot\theta=\frac{1}{1/\sqrt3}\\\\\cot\theta=\sqrt3\end{gathered}

cotθ=

tanθ

1

cotθ=

1/

3

1

cotθ=

3

Substituting these values in the given expression

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

(tanθ+cotθ)

2

=(

3

1

+

3

)

2

=(

3

4

+3)

2

=

3

16

#Learn More:

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

pls follow me