This class 10 Maths extra practice question is from chapter 8 - Introduction to Trigonometry. Concept Covered: Computing the value of angle by solving a trigonometric expression using Componendo Dividendo Rule. Level of difficulty: Hard

Question 14: If θ is an acute angle and \\frac{\text{sinθ + 1}}{\text{sinθ − 1}}) =\\frac{\sqrt{3} + 2}{\sqrt{3} - 2}), find θ

online.maxtute.com

If \\frac{\text{P}}{\text{Q}}) = \\frac{\text{R}}{\text{S}}) , then \\frac{\text{P + Q}}{\text{P - Q}})= \\frac{\text{R + S}}{\text{R - S}})

\\frac{\text{sin θ + 1}}{\text{sin θ − 1}}) =\\frac{\sqrt{3} + 2}{\sqrt{3} - 2}) becomes \\frac{\text{(sin θ + 1) + (sin θ − 1)}}{\text{(sin θ + 1) − (sin θ − 1)}}) = \\frac{(\sqrt{3}+ 2) + (\sqrt{3} − 2)}{(\sqrt{3}+ 2) - (\sqrt{3} − 2)})

\\frac{\text{2 sin θ }}{\text{2}})= \\frac{2 × \sqrt{3}}{\text{4}})

sin θ = \\frac{\sqrt{3}}{\text{2}})

We know that, sin 60° = \\frac{\sqrt{3}}{\text{2}})

∴ sin θ = sin 60°

**θ = 60°**

Divide both numerator and denominator of RHS by 2:

\\frac{\frac{\sqrt{3} + 2}{2}}{\frac{\sqrt{3} - 2}{2}}) = \\frac{\frac{\sqrt{3}}{2} + 1 }{\frac{\sqrt{3}}{2} - 1 })

sin 60° = \\frac{\sqrt{3}}{2})

∴ \\frac{\frac{\sqrt{3}}{2} + 1 }{\frac{\sqrt{3}}{2} - 1 }) =\\frac{\text{sin 60° + 1}}{\text{sin 60° − 1}})

Compare the above result with LHS

\\frac{\text{ sin θ + 1 }}{\text{sin θ -1 }}) = \\frac{\text{ sin 60 ° + 1}}{\text{sin 60 ° − 1}})

∴ sin θ = sin 60°

**θ = 60°**

Class 10 Maths

Register in 2 easy steps and

Start learning in 5 minutes!

CBSE Class 10 Maths - 2021

- Real Numbers Revision Class
- Polynomials Revision Videos
- Linear Equations Revision Class
- Quadratic Equations Revision Class
- Arithmetic Progressions Revision Video
- Triangles Revision
- Coordinate Geometry Revision
- Trigonometry Revision Class
- Appl of Trigonometry
- Circles Revision Class
- Areas Related to Circles Revision Videos

1. Trigonometric Ratios | CBSE Class 10 Extra Practice Question #01 | Easy Question ** Questions 1 ** ▶

2. Trigonometric Ratios | CBSE Class 10 Math Additional Practice Question #02 | Easy Question ** Question 2** ▶

3. Trigonometric values | CBSE Class 10 Math Extra Question #03 | Medium Question ** Question 3** ▶

4. Trigonometry theory & practice | CBSE 10th Extra Practice Question #04 | Medium Question ** Question 4** ▶

5. Trigonometric Ratios | CBSE 10th Extra Practice Question #05 | Easy Question ** Question 5** ▶

6. Trigonometry & Quadratic Equation | CBSE 10th Extra Practice Question #06 | Medium Question ** Question 6** ▶

7. Trigonometric values| CBSE 10th Extra Practice Question #07 | Easy Question ** Question 7** ▶

8. Trigonometric Ratios | CBSE 10th Extra Practice Question #08 | Easy Question ** Question 8** ▶

9. Trigonometric values | CBSE 10th Extra Practice Question #09 | Easy Question ** Question 9** ▶

10. Trigonometric values | CBSE 10th Extra Practice Question #10 | Easy Question ** Question 10** ▶

11. Square of Trigonometric Ratios | CBSE Class 10 Extra Question #11 | Easy Question ** Question 11** ▶

12. Trigonometric values | CBSE 10th Extra Practice Question #12 | Easy questions ** Question 12** ▶

13. Trigonometric Values of Basic Angles | CBSE 10th Extra Question #13 | Easy question ** Question 13** ▶

14. Trigonometric Ratios of Specific Values | CBSE Class 10 Important Question #14 | Hard Question ** Question 14** ▶

15. Trigonometric Ratio & Linear Equations | CBSE Class 10 Important Question #15 | Hard Question ** Question 15** ▶

Copyrights © 2016 - 22 All Rights Reserved by Maxtute.com - An Ascent Education Initiative.

Privacy Policy | Terms & Conditions

**Mobile:** (91) 93822 48484

**WhatsApp:** WhatsApp Now

**Email:** learn@maxtute.com