Question

$\sf \: Question:−​​$


Find the value of θ in each of the following. θ is an acute angle.


(i) 3 sec 2θ = 2√3 (ii) 4 cot 3θ - 4 = 0 (iii) 2 sin 2θ = 1


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Answer 1

GIVEN★

• (i) 3 sec 2θ = 2√3

• (ii) 4 cot 3θ - 4 = 0

• (iii) 2 sin 2θ = 1

find★

value of θ=?

EVALUATION★

let θ =a

• (i) 3 sec 2a = 2√3

• $= > 3 \sec(2a) = 2 \sqrt{3} \\ \\ = > \sec(2a) = \frac{2 \sqrt{3} }{3} \\ \\ = > \sec(2a) = \frac{2 \sqrt{3} }{ \sqrt{3} \sqrt{3} } \\ \\ = > sec(2a) = \frac{2}{ \sqrt{3} }$

• we know that
• $= > \sec(30) = \frac{2}{ \sqrt{3} }$
• to
• $\sec(2a) = sec(30)$

• comparison

$= > 2a = 30 \\ \\ = > a = \frac{30}{2} \\ \\ = > a = 15$

===================

(ii) 4 cot 3a - 4 = 0

• $= > 4\cot(3a) = 4 \\ \\ = > \cot(3a) = \frac{4}{4} \\ \\ = > \cot(3a) = 1$
• we know that

$= > \cot(45) = 1$

$= > \cot(3a) = \cot(45)$

• coparision

$= > 3a = 45 \\ \\ = > a = \frac{45}{3} \\ \\ = > a = 15$

=============

(iii) 2 sin 2a = 1

• $= \sin(2a) = \frac{1}{2}$
• we know that

$= > \sin(30) = \frac{1}{2}$

to

$= > \sin(2a) = \sin(30)$

cmparision

$= > 2a = 30 \\ \\ = > a = \frac{30}{2} \\ \\ = > a = 15$

====================================

★★answer

θ=15° ✅

=======================

I hope it helps you

Answer 2

Answer:

♣ $\tt \red{\underline{\underline{Given \: Question}}}$

Find the value of θ in each of the following. (θ is an acute angle.)

(i) sec 2θ = 2/√3

(ii) 4 cot 3θ - 4 = 0

(iii) 3 tan² θ + 2 = 3

$\purple{\rule{45pt}{7pt}}\red{\rule{45pt}{7pt}}\pink{\rule{45pt}{7pt}}\blue{\rule{45pt}{7pt}}$

Given:

(i) sec 2θ = 2/√3

(ii) 4 cot 3θ - 4 = 0

(iii) 3 tan² θ + 2 = 3

To find:

The value of the θ.

Solution:

(i) sec 2θ = 2/√3

sec 2θ = sec 30°

2θ = 30°

θ = 15°

$\purple{\rule{45pt}{7pt}}\red{\rule{45pt}{7pt}}\pink{\rule{45pt}{7pt}}\blue{\rule{45pt}{7pt}}$

(ii) 4 cot 3θ - 4 = 0

4 cot 3θ = 4

cot 3θ = 1

cot 3θ = cot 45°

3θ = 45°

θ = 15°

$\purple{\rule{45pt}{7pt}}\red{\rule{45pt}{7pt}}\pink{\rule{45pt}{7pt}}\blue{\rule{45pt}{7pt}}$

(iii) 3 tan² θ + 2 = 3

3 tan² θ = 3-2

3 tan² θ =1

tan² θ = 1/3

tanθ = √1/3

tanθ = 1/√3

tanθ = tan 30°

θ = 30°

$\purple{\rule{45pt}{7pt}}\red{\rule{45pt}{7pt}}\pink{\rule{45pt}{7pt}}\blue{\rule{45pt}{7pt}}$

♣ Final Answer :-

$\boxed{\tt \red{(i) θ = 15}}$

$\boxed{\tt \red{(ii) θ = 15}}$

$\boxed{\tt \red{(iii) θ = 30}}$

$\purple{\rule{45pt}{7pt}}\red{\rule{45pt}{7pt}}\pink{\rule{45pt}{7pt}}\blue{\rule{45pt}{7pt}}$

HOPES IT HELPS YOU :)