This 2019 CBSE class 10 Maths 4 mark question is from Trigonometry. Concept: Expressing trigonometric ratios in terms of sin θ and cos θ and solving a quadratic equation using the quadratic formula.

Question 30: If sec θ + tan θ = p, then find the value of cosec θ.

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sec θ + tan θ = p

\\frac{1}{\text{cos θ}})+ \\frac{\text{sin θ}}{\text{cos θ}}) = p

\\frac{\text{1 + sin θ }}{\text{cos θ}}) = p

1 + sin θ = p(cos θ)

Substitute cos θ = \\sqrt{1 – {sin}^{2}θ})

1 + sin θ = p\\sqrt{1 – {sin}^{2}θ})

Square both sides of the equation: (1 + sin θ)^{2} = p^{2}(1 - sin^{2}θ)

1 + sin^{2} θ + 2 sin θ = p^{2} - p^{2} sin^{2} θ

**(1 + p ^{2}) sin^{2} θ + 2 sin θ + (1 – p^{2}) = 0**

Roots of a quadratic equation ax^{2} + bx + c = 0 are,

\\frac{−b ± \sqrt{b^2 - 4ac}}{2a})

Compute Discriminant, D: D = b^{2} - 4ac

In the equation, (1 + p^{2}) sin^{2} θ + 2 sin θ + (1 – p^{2}) = θ, a = (1 + p^{2}); b = (2); c = (1 – p^{2})

Discriminant, D = 4 – 4(1 + p^{2})(1 – p^{2})

= 4 – 4(1 – p^{4}) = 4p^{4}

Substitute the value of D,

The root, sin θ = \\frac{−2 ± √4p^4}{ 2(1 + p^2)}) = \\frac{−1 ± p^2}{(1 + p^2)}) = \\frac{p^2 − 1}{p^2 + 1}) , -1

**cosec θ = \\frac{\text{1}}{\text{sin θ}}) = \\frac{p^2 + 1}{p^2 − 1}) , -1**

Class 10 Maths

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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. Section A | 2018 CBSE Class 10 Maths 1 Mark **Questions 1 to 2** ▶

2. Section A | 2019 CBSE Class 10 Maths 1 Mark **Question 3 to 4** ▶

3. Section A | 2019 CBSE Class 10 Maths 1 Mark **Question 5 to 6** ▶

4. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 7** | Real Numbers ▶

5. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 8** | Arithmetic Progressions ▶

6. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 9** | Coordinate Geometry ▶

7. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 10** | Probability ▶

8. Section B | 2019 CBSE Class 10 Maths 3 Mark **Question 11** | Probability ▶

9. Section B | 2019 CBSE Class 10 Maths 3 Mark **Question 12** | Linear Equations ▶

10. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 13** | Real Numbers & HCF ▶

11. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 14** | Polynomials ▶

12. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 15** | Linear Equations ▶

13. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 16** | Coordinate Geometry ▶

14. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 17** | Trigonometric Ratios ▶

15. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 18** | Circles ▶

16. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 19** | Triangles ▶

17. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 20** | Areas Related to Circles ▶

18. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 21** | Statistics - Median ▶

19. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 22** | Statistics ▶

20. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 23** | Quadratic Equations ▶

21. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 24** | Arithmetic Progressions ▶

22. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 25** | Triangles ▶

23. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 27** | Trigonometry ▶

24. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 28** | Statistics ▶

25. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 29** | Surface Areas ▶

26. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 30** | Trigonometry ▶

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