Question

Find the value of θ. θ is an acute angle.

3 sec 2θ = 2√3​

Answer 1

Answer:

Step-by-step explanation:

sec2θ = 2√3 / 3 =  2 / √3   ( we know sec 30° = 2 / √3 )

2θ = 30°

θ = 15°

Answer 2

Solution →

$3 \sec(2\theta) = 2 \sqrt{3}$

$\sec(2\theta) = \frac{2 \sqrt{3} }{3}$

We can write √3 as √3×√3 ,

$\sec(2\theta) = \frac{2 \sqrt{3} }{ \sqrt{3 } \times \sqrt{3} }$

√3 will be cancelled by √3 ,

$\sec(2\theta) = \frac{2}{ \sqrt{3} }$

we know that →

• $\frac{2}{ \sqrt{3} } = \sec(30)$

So ,

$\sec(2\theta) = \sec(30)$

$2\theta \: = 30$

$\theta \: = \frac{30}{2}$

$\boxed{\theta \: = \: 15}$

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