Question

tan 22° + tan 38° – root 3 = k tan 22°.tan38° then k=​?

Answer 1

Answer:

$k = - \sqrt{3}$

Answer 2

Answer:

The value of k is 1.35455264.

Given Data:

Tan 22° + Tan 38° – root 3 = k Tan 22°. Tan38°

To Find:

Calculate the value of k.

Step-By-Step Explanation:

Step 1:

The equation as $tan (22 \tan (38))$

$=\tan (22+\tan (38-\sqrt{3})) \{ktan}(22 \tan (38))=\tan (22+\tan (38-3))$

$\begin{aligned} \{ktan}(22 \tan (38)) &=\tan (22+\tan (38-\sqrt{3})) \{ktan}(22 \tan (38)) \\ &=\tan (22+\tan (38-3)) \end{aligned}$

Step 2:  

Evaluate$\tan (38) \tan (38)$

$\begin{aligned} \{ktan}(22 \cdot 0.78128562) &=\tan (22+\tan (38-\sqrt{3})) \{ktan}(22 \cdot 0.78128562) \\ &=\tan (22+\tan (38-3)) \end{aligned}$

Step 3:

Multiply 2222 by 0.781285620.78128562.

$\begin{aligned} k \tan (17.18828378) &=\tan (22+\tan (38-\sqrt{3})) k \tan (17.18828378) \\ &=\tan (22+\tan (38-3)) \end{aligned}$

Divide each term by tan (17.18828378) tan (17.18828378) and simplify.

Step 4:

$\begin{aligned} k=\tan (22.73371214) \cot (17.18828378) k & =&\tan (22.73371214) \cot (17.18828378) \end{aligned}$

The result can be shown in multiple forms.

Step 5:

Exact Form:

$k=tan (22.73371214) cot (17.18828378) k=tan (22.73371214) cot (17.18828378)$

Step 6:

Result:

Decimal Form:

The value of k=1.35455264.