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

Last updated at Dec. 16, 2024 by Teachoo

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

(a) 0   (b) 2   (c) 20   (d) 2 20

Transcript

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

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