Question

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Answer 1

Given that:-

tan5θ /2 = $\sf\sqrt{3}$

To find :-

2θ

Solution :-

As we know that ,

tan60° = $\sf\sqrt{3}$

So ,

tan5θ/2= tan60°

In both sides tan are there

Then comparing angles

$\sf\dfrac{5θ}{2}$ = 60°

Do cross multiplication

5θ = 60(2)

5θ = 120°

θ = 120°/5

θ = 24°

Now, we have to find

2θ = 2 (24°)

2θ = 48°

______________________________

Know more :-

Trignometric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

Trignometric relations

sinθ = 1/cscθ

cosθ = 1 /secθ

tanθ = 1/cotθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Trignometric ratios

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

cotθ = adj/opp

cscθ = hyp/opp

secθ = hyp/adj

Trignometric table :-

$\bullet\:\sf Trigonometric\:Values :\\\\\boxed{\begin{tabular}{c|c|c|c|c|c}Radians/Angle & 0 & 30 & 45 & 60 & 90\\\cline{1-6}Sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1\\\cline{1-6}Cos \theta & 1 & \dfrac{\sqrt{3}}{2}& \dfrac{1}{\sqrt{2}}& \dfrac{1}{2}&0\\\cline{1-6}Tan \theta&0& \dfrac{1}{\sqrt{3}}&1&\sqrt{3}&Not D{e}fined\end{tabular}}$

Answer 2

Answer:

Answer is 48°

Step-by-step explanation:

We Have :-

$\tan( \dfrac{5 \theta}{2} ) = \sqrt{3}$

To Find :-

$value \: of \: 2 \theta$

Value Used :-

$\tan(60) = \sqrt{3}$

Solution :-

$\tan( \dfrac{5 \theta}{2} ) = \sqrt{3} \\ \\ we \: know \: that \: \tan(60) = \sqrt{3} \\ \\ putting \: this \: in \: above \: equation \\ \\ \dfrac{5 \theta}{2} = 60 \\ \\ 5\theta = 60 \times 2 \\ \\ 5\theta = 120 \\ \\ \theta = \dfrac{120}{5} \\ \\ \theta = 24 \\ \\ we \: have \: to \: find \: 2\theta \\ \\ 2 \times \theta = 2 \times 24 = 48$

Answer is 48°