Question 23 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ] - Solutions of Sample Papers for Class 10 Boards

Last updated at May 29, 2023 by Teachoo

If tan⁡α + cot⁡α = 2, then tan⁡20α + cot⁡20α =

(a) 0 (b) 2 (c) 20 (d) 2 ²⁰

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Question 23 If tan⁡𝛼 + cot⁡𝛼 = 2, then tan⁡20𝛼 + cot⁡20𝛼 = (a) 0 (b) 2 (c) 20 (d) 220Given tan⁡𝛼 + 𝒄𝒐𝒕⁡𝜶 = 2 tan⁡𝛼 + 𝟏/𝐭𝐚𝐧⁡𝜶 = 2 (〖𝑡𝑎𝑛〗^2⁡𝛼 + 1)/tan⁡𝛼 = 2 〖𝑡𝑎𝑛〗^2⁡𝛼 + 1 = 2 𝑡𝑎𝑛⁡𝛼 〖𝑡𝑎𝑛〗^2⁡𝛼 −"2" 𝑡𝑎𝑛⁡𝛼+ 1 = 0 〖𝒕𝒂𝒏〗^𝟐⁡𝜶 −"2" 𝒕𝒂𝒏⁡𝜶+ 𝟏^𝟐 = 0 (𝒕𝒂𝒏⁡𝜶 −𝟏)^𝟐 = 0 Therefore, 𝒕𝒂𝒏⁡𝜶 = 1 Thus, 𝛼 = 45° Now, 〖𝒕𝒂𝒏〗^𝟐𝟎⁡𝜶 + 〖𝒄𝒐𝒕〗^𝟐𝟎⁡𝜶 = tan^20⁡〖45°〗 + cot^20⁡〖45° 〗 = 1^20+1^20 = 1+1 = 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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