Question

Solve the trigonometric equation: $\sf\displaystyle tan3x={\frac{1}{tan2x}}$
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Answer 1

Answer:

0.58 [The value of tan (30)]

Step-by-step explanation:

Tan(3x)=1

Then you can deduce that Tan^-(1)=3x.

Then you see that Tan(45)=1. thus 3x=45 degrees. you can divide both sides by 3 resulting x=15 degrees.

Your question is asking what tan(2x) is, which is the same as tan(30). Finally, we find the value of tan(30), which can be found by dividing sin(30) by cos(30).

So,

The answer is ~ 0.58 [the value of tan(30)].

Hope it Help's you Friend ... !

Answer 2

Answer:

18° + k(π/5)

Step-by-step explanation:

Notice that 1/tan3x = cot2x

From the basic properties of trigonometry: cotA = tan(90 - A)

Therefore, cot2x = tan(90 - 2x)

Thus,

=> tan3x = tan(90 - 2x)

=> 3x = 90 - 2x

Since tanx is periodic in π, it be:

=> 3x = 90 - 2x + kπ, k be any constant

=> 5x = 90 + kπ

=> x = 18° + k(π/5) or,

=> x = π/10 + k(π/5) , where k € Z, x ≠ kπ/2, x ≠ (π/6) + k(π/3).

In 180°, x can be

• π/10 = 18°

• π/10 + 1(π/5) = 54°

• π/10 + 3(π/5) = 126°

• π/10 + 4(π/5) = 162°

*k = 2 is neglected as for k = 2, x is 90, tan3x is undefined.