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Question 8 - CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 13, 2024 by Teachoo

If sin θ + cos θ = √2, then tan θ + cot θ =

(a) 1   (b) 2   (c) 3   (d) 4

 

This question is Similar to Question 8 CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard

 

 

Transcript

Question 8 If sin θ + cos θ = √2, then tan θ + cot θ = (a) 1 (b) 2 (c) 3 (d) 4 Now, tan 𝜃 + cot 𝜃 = sin⁡𝜃/cos⁡𝜃 +cos⁡𝜃/sin⁡𝜃 = (〖𝒔𝒊𝒏〗^𝟐⁡𝜽 + 〖𝒄𝒐𝒔〗^𝟐⁡𝜽)/(cos⁡𝜃 sin⁡𝜃 ) Putting sin2 𝜃 + cos2 𝜃 = 1 = 𝟏/(𝒄𝒐𝒔⁡𝜽 𝒔𝒊𝒏⁡𝜽 ) Finding cos θ sin θ sin 𝜃 + cos 𝜃 = √2 Squaring both sides (sin 𝜃 + cos 𝜃)2 = (√3)^2 (sin 𝜃 + cos 𝜃)2 = 2 sin2 𝜃 + cos2 𝜃 + 2 sin θ cos θ = 2 Putting sin2 𝜃 + cos2 𝜃 = 1 1 + 2 sin θ cos θ = 2 2 sin θ cos θ = 2 – 1 2 sin θ cos θ = 1 sin θ cos θ = 1/2 cos θ sin θ = 𝟏/𝟐 Now, tan 𝜃 + cot 𝜃 = 1/(𝑐𝑜𝑠⁡𝜃 𝑠𝑖𝑛⁡𝜃 ) Putting values = 1/(1/2) = 2 So, the correct answer is (b)
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo