CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard
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CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard
Last updated at April 16, 2024 by Teachoo
This question is Similar to Question 8 CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard
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 = sin𝜃/cos𝜃 +cos𝜃/sin𝜃 = (〖𝒔𝒊𝒏〗^𝟐𝜽 + 〖𝒄𝒐𝒔〗^𝟐𝜽)/(cos𝜃 sin𝜃 ) Putting sin2 𝜃 + cos2 𝜃 = 1 = 𝟏/(𝒄𝒐𝒔𝜽 𝒔𝒊𝒏𝜽 ) 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/(𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝜃 ) Putting values = 1/(1/2) = 2 So, the correct answer is (b)
