Question 26 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Basic [MCQ] - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 16, 2024 by Teachoo

Given that sin 𝜃 = a/b, then tan 𝜃 is equal to

(a) b/√(a ² + b ² ) (b) b/√(b ² - a ² ) (c) a/√(a ² + b ² ) (d) b/√(b^ ² + a ² )

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Transcript

Question 26 Given that sin 𝜃 = 𝑎/𝑏, then tan 𝜃 is equal to (a) 𝑏/√(𝑎^2 + 𝑏^2 ) (b) 𝑏/√(𝑏^2 − 𝑎^2 ) (c) 𝑎/√(𝑎^2 + 𝑏^2 ) (d) 𝑏/√(𝑏^2 + 𝑎^2 ) Let Δ ABC be the right angled triangle Given sin 𝜃 = 𝒂/𝒃 Since sin 𝜃 = 𝑶𝒑𝒑𝒐𝒔𝒊𝒕𝒆/𝑯𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 Therefore, BC = a, AC = b Finding side AB By Pythagoras theorem AC2 = AB2 + BC2 b2 = AB2 + a2 b2 − a2 = AB2 AB2 = b2 − a2 AB = √(𝒃^𝟐−𝒂^𝟐 ) Now, tan 𝜃 = 𝐵𝐶/𝐴𝐵 = 𝒂/√(𝒃^𝟐 − 𝒂^𝟐 ) So, the correct answer is (d)

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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

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