Question 17 (Or 2nd) - CBSE Class 10 Sample Paper for 2019 Boards - Solutions of Sample Papers for Class 10 Boards

Last updated at March 23, 2023 by Teachoo

Question 17 (OR 2 nd question)

Prove that sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + cosec θ

Question 17 (Or 2nd) - CBSE Class 10 Sample Paper for 2019 Boards - Part 2

Question 17 (Or 2nd) - CBSE Class 10 Sample Paper for 2019 Boards - Part 3

Get live Maths 1-on-1 Classs - Class 6 to 12

Book 30 minute class for ~~₹ 499~~ ₹ 299

Transcript

Question 17 (OR 2nd question) Prove that sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + cosec θ Solving LHS sin θ (1 + tan θ) + cos θ (1 + cot θ) = sin θ (1 + sin⁡𝜃/cos⁡𝜃 ) + cos θ (1 + cos⁡𝜃/sin⁡𝜃 ) = sin θ ((cos⁡𝜃 + sin⁡𝜃)/cos⁡𝜃 ) + cos θ ((sin⁡𝜃 + cos⁡𝜃)/sin⁡𝜃 ) Taking cos⁡𝜃 + sin⁡𝜃 common = (cos⁡𝜃 + sin⁡𝜃) (sin⁡𝜃/cos⁡𝜃 +cos⁡𝜃/sin⁡𝜃 ) = (cos⁡𝜃 + sin⁡𝜃) ((sin⁡𝜃 × sin⁡𝜃 + cos⁡𝜃 × cos⁡𝜃)/(cos⁡𝜃 sin⁡𝜃 )) = (cos⁡𝜃 + sin⁡𝜃) ((sin^2⁡𝜃 + cos^2⁡𝜃 )/(cos⁡𝜃 sin⁡𝜃 )) Since sin^2⁡𝜃 + cos^2⁡𝜃 = 1 = (cos⁡𝜃 + sin⁡𝜃) ((1 )/(cos⁡𝜃 sin⁡𝜃 )) = (cos⁡𝜃 )/(cos⁡𝜃 sin⁡𝜃 ) + (sin⁡𝜃 )/(cos⁡𝜃 sin⁡𝜃 ) = (1 )/sin⁡𝜃 + (1 )/cos⁡𝜃 = cosec θ + sec θ = RHS Thus LHS = RHS Hence proved

Next: Question 18 Important → Ask a doubt

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular