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

Answer 1

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 [correct question]

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°

(ii) 4 cot 3θ - 4 = 0

4 cot 3θ = 4

cot 3θ = 1

cot 3θ = cot 45°

3θ = 45°

θ = 15°

(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°

Answer 2

Step-by-step explanation:

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