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

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Last updated at Oct. 1, 2019 by Teachoo

**
Question 30
**

If sec θ + tan θ = p, then find the value of cosec θ

Subscribe to our Youtube Channel - https://you.tube/teachoo

Transcript

Question 30 If sec θ + tan θ = p, then find the value of cosec θ Given sec θ + tan θ = p Converting sec θ and tan θ in sin θ and cos θ 1/cos𝜃 + sin𝜃/cos𝜃 = p (1 + sin𝜃)/cos𝜃 = p We need to find cosec θ, To find cosec θ , we convert everything into sin θ So, we square both sides ((1 + sin𝜃)/cos𝜃 )^2 = p2 (1^2 + sin^2𝜃 + 2 sin𝜃)/cos^2𝜃 = p2 1 + sin2 θ + 2 sin θ = p2 × cos2 θ Now, sin2 θ + cos2 θ = 1 cos2 θ = 1 – sin2 θ 1 + sin2 θ + 2 sin θ = p2 × (1 – sin2 θ) 1 + sin2 θ + 2 sin θ = p2 – p2 sin2 θ Let x = sin θ 1 + x2 + 2x = p2 – p2 x2 x2 + p2 x2 + 2x + 1 – p2 = 0 (1 + p2) x2 + 2x + (1 – p2) = 0 Comparing with ax2 + bx + c a = (1 + p2) , b = 2, c = (1 – p2) Now, x = (−𝑏 ± √(𝑏^2 − 4𝑎𝑐))/2𝑎 x = (−2 ± √(2^2 − 4 × (1 + 𝑝^2 ) × (1 − 𝑝^2 ) ))/2(1 + 𝑝^2 ) x = (−2 ± √(4 − 4 × (1 + 𝑝^2 ) × (1 − 𝑝^2 ) ))/2(1 + 𝑝^2 ) x = (−2 ± √4 √(1 − (1 + 𝑝^2 ) × (1 − 𝑝^2 ) ))/2(1 + 𝑝^2 ) x = (−2 ± 2 √(1 − (1 + 𝑝^2 ) × (1 − 𝑝^2 ) ))/2(1 + 𝑝^2 ) x = (−1 ± √(1 − (1 + 𝑝^2 ) × (1 − 𝑝^2 ) ))/((1 + 𝑝^2 ) ) x = (−1 ± √(1 − (1^2 −(𝑝^2 )^2 ) ))/((1 + 𝑝^2 ) ) x = (−1 ± √(1 − (1 − 𝑝^4 ) ))/((1 + 𝑝^2 ) ) x = (−1 ± √(1 − 1 + 𝑝^4 ))/((1 + 𝑝^2 ) ) x = (−1 ± √(𝑝^4 ))/((1 + 𝑝^2 ) ) x = (−1 ± 𝑝^2)/((1 + 𝑝^2 ) ) Putting x = sin θ sin θ = (−1 ± 𝑝^2)/((1 + 𝑝^2 ) ) For + sin θ = (−1 + 𝑝^2)/((1 + 𝑝^2 ) ) sin θ = (𝑝^2 − 1)/(𝑝^2 + 1) Therefore, cosec θ = 1/sin𝜃 = (𝒑^𝟐 + 𝟏)/(𝒑^𝟐 − 𝟏) For – sin θ = (−1 − 𝑝^2)/((1 + 𝑝^2 ) ) sin θ = (−(1 + 𝑝^2))/((1 + 𝑝^2 ) ) sin θ = –1 Therefore, cosec θ = 1/sin𝜃 = 1/(−1) = –1

CBSE Class 10 Sample Paper for 2019 Boards

Paper Summary

Question 1

Question 2 (Or 1st)

Question 2 (Or 2nd)

Question 3 (Or 1st)

Question 3 (Or 2nd)

Question 4

Question 5

Question 6

Question 7 (Or 1st)

Question 7 (Or 2nd)

Question 8 (Or 1st)

Question 8 (Or 2nd)

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16 (Or 1st)

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Question 17 (Or 2nd)

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Question 19 (Or 1st)

Question 19 (Or 2nd)

Question 20

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Question 21 (Or 2nd)

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Question 23 (Or 1st)

Question 23 (Or 2nd)

Question 24

Question 25

Question 26

Question 27 (Or 1st)

Question 27 (Or 2nd)

Question 28 (Or 1st)

Question 28 (Or 2nd)

Question 29

Question 30 You are here

Class 10

Solutions of Sample Papers for Class 10 Boards

- CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard
- CBSE Class 10 Sample Paper for 2021 Boards - Maths Basic
- CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard
- CBSE Class 10 Sample Paper for 2020 Boards - Maths Basic
- CBSE Class 10 Sample Paper for 2019 Boards
- CBSE Class 10 Sample Paper for 2018 Boards

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.