Question

If for some angle theta , cot 2theta =1/root3, then find the value of sin 3 theta, where 2 theta < 90°

Answer 1

cot2theta=1/
$\sqrt{3 }$
cot 2theta= cot60
therefore 2theta=60
theta= 30

sin3theta=sin90=1

Answer 2

Answer:

For θ = 30°, the value of sin3θ = 1.

Step-by-step explanation:

Given for some angle θ,

    $cot2\theta=\dfrac{1}{\sqrt{3} }$                ....(1)

As we know from the trigonometric values,

$cot60^{o} =\dfrac{1}{\sqrt{3} }$                  ....(2)

Combining equations (1) and (2), we get

$cot2\theta=cot60^{o}$

$\implies 2\theta=60^{o}$

which satisfies the given condition, $2\theta < 90^{o}$.

Now solving for the value of angle θ,

$\implies \theta=\frac{60}{2} =30^{o}$

Substituting the value of angle θ in

$sin 3 \theta=sin 3 \times 30^{o} =sin 90^{o}$

Again from the trigonometric values, we have $sin 90^{o}=1$

Therefore, for θ = 30°, the value of sin3θ = 1.