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

Last updated at April 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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