Trigonometry Important Question 10

This class 10 Maths additional practice question is from the topic Trigonometry. Concept Tested: Trigonometric values of basic angles.

Question 10 : 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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Video Explanation

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Explanatory Answer | Trigonometry Important Questio 10

(i) 3 sec 2θ = 2√3

sec 2θ = \\frac{2\sqrt{3}}{3})= \\frac{2}{\sqrt{3}})
We know sec 30° = \\frac{2}{\sqrt{3}})
sec 2θ = sec 30°
2θ = 30° or θ = 15°

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(ii) 4 cot 3θ- 4 = 0

4 cot 3θ = 4
cot 3θ = 1
We know cot 45° = 1
∴ cot 3θ = cot 45°
So, 3θ = 45° or θ = 15°

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(iii) 2 sin 2θ = 1

sin 2θ =\\frac{1}{2})
We know sin 30° = \\frac{1}{2})
∴ sin 2θ = sin 30°
So, 2θ = 30° or θ = 15°