Question

if 3 tan theta equal to 4 then write the value of tan theta + cot theta​

Answer 1

$\huge{\boxed{\boxed{\mathfrak{\red{Answer:-}}}}}$

${\bold{\underline{\underline{Given:-}}}}$

$\to\ 3Tanθ =4$

${\bold{\underline{\underline{To \: find :-}}}}$

$\to\ Tanθ+cotθ$

${\bold{\underline{\underline{Solution :-}}}}$

$\implies\ 3Tanθ=4 \\ \\ \implies\ Tanθ = 3/4$

Also;

$\implies\cotθ = \frac {1}{Tanθ} \\ \\ \implies\ cotθ= \frac {1}{3/4} \\ \\ \implies\ cotθ= \frac{3}{4}$

Now,

$\implies\ Tanθ + cotθ= ? \\ \\ \implies\ 4/3 +3/4 \\ \\ \implies\ 16+ 9/12\\ \\ \implies\ \frac {25}{12}$

$\mathbb\pink{Thanks....}$

Answer 2

The value of $\tan \theta+\cot \theta$$=\dfrac{25}{12}$

Step-by-step explanation:

We have,

$3\tan \theta=4$

⇒ $\tan \theta=\dfrac{4}{3}$

To find, the value of $\tan \theta+\cot \theta=?$

∴ $\tan \theta+\cot \theta$

$=\tan \theta+\dfrac{1}{\tan \theta}$

Using the trigonometric identity,

$\cot \theta=\dfrac{1}{\tan \theta}$

Put $\tan \theta=\dfrac{4}{3}$, we get

$=\dfrac{3}{4} +\dfrac{1}{\dfrac{3}{4}}$

$=\dfrac{3}{4} +\dfrac{4}{3}$

$=\dfrac{9+16}{12}$

$=\dfrac{25}{12}$

∴ The value of $\tan \theta+\cot \theta$$=\dfrac{25}{12}$