Question

If tan 22 +tan 38 +√3=k tan22 tan 38 then k=

Answer 1

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(22tan(38))

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

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

Step 2:

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

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

Step 3:

Multiply 2222 by 0.781285620.78128562.

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

ktan(17.18828378)

=tan(22+tan(38−

3

))ktan(17.18828378)

=tan(22+tan(38−3))

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}

k=tan(22.73371214)cot(17.18828378)k

=

tan(22.73371214)cot(17.18828378)

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)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.

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