Extra Questions For Class 10 Maths Trigonometry | Q11

This class 10 Maths additional Practice Question is from the chapter Introduction to Trigonometry. It tests the concept of trigonometric ratios, squares of trigonometric ratios, and trigonometric values of specific angles.

Question 11 : Solve the following: 0° < θ < 90°
(i) 2 sin² θ = \\frac{3}{2})
(ii) 3 tan² θ + 2 = 3
(iii) cos² θ - \\frac{1}{4})= \\frac{1}{2})

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Video Explanation

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Explanatory Answer | Trigonometry Important Question 11

(i) 2 sin² θ = \\frac{3}{2})

sin² θ = \\frac{3}{4})
sin θ = \\frac{√3}{2})
We know sin 60° = \\frac{√3}{2})
∴ sin θ = sin 60° or θ = 60°

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(ii) 3 tan² θ + 2 = 3

3 tan² θ = 1
tan² θ = \\frac{1}{3}) or tan θ = \\frac{1}{√3})
We know tan 30° = \\frac{1}{√3})
∴ tanθ = tan 30° or θ = 30°

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(iii) cos² θ - \\frac{1}{4})= \\frac{1}{2})

cos² θ = \\frac{1}{2}) + \\frac{1}{4}) =\\frac{3}{4})
cosθ =\\frac{√3}{2})
We know cos 30° = \\frac{√3}{2})
∴ cosθ = cos 30° or θ = 30°