If tanα + cotα = 2, then tan20α + cot20α =
(a) 0 (b) 2 (c) 20 (d) 2 ^{ 20 }
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Last updated at Sept. 6, 2021 by Teachoo
Transcript
Question 23 If tan𝛼 + cot𝛼 = 2, then tan20𝛼 + cot20𝛼 = (a) 0 (b) 2 (c) 20 (d) 220Given tan𝛼 + 𝒄𝒐𝒕𝜶 = 2 tan𝛼 + 𝟏/𝐭𝐚𝐧𝜶 = 2 (〖𝑡𝑎𝑛〗^2𝛼 + 1)/tan𝛼 = 2 〖𝑡𝑎𝑛〗^2𝛼 + 1 = 2 𝑡𝑎𝑛𝛼 〖𝑡𝑎𝑛〗^2𝛼 −"2" 𝑡𝑎𝑛𝛼+ 1 = 0 〖𝒕𝒂𝒏〗^𝟐𝜶 −"2" 𝒕𝒂𝒏𝜶+ 𝟏^𝟐 = 0 (𝒕𝒂𝒏𝜶 −𝟏)^𝟐 = 0 Therefore, 𝒕𝒂𝒏𝜶 = 1 Thus, 𝛼 = 45° Now, 〖𝒕𝒂𝒏〗^𝟐𝟎𝜶 + 〖𝒄𝒐𝒕〗^𝟐𝟎𝜶 = tan^20〖45°〗 + cot^20〖45° 〗 = 1^20+1^20 = 1+1 = 𝟐 So, the correct answer is (b)
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CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ]
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