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

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.