Question 32 - 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

In the given figure, D is the mid-point of BC, then the value of cot 𝑦 ° cot 𝑥 ° is

(a) 2 (b) 1/2 (c) 1/3 (d) 1/4

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Transcript

Question 32 In the given figure, D is the mid-point of BC, then the value of cot 𝑦 ° cot 𝑥 ° is (a) 2 (b) 1/2 (c) 1/3 (d) 1/4 Since D is mid-point of BC Let CD = BD = a Now, 𝒄𝒐𝒕⁡〖𝒚°〗/𝒄𝒐𝒕⁡〖𝒙°〗 = (1/tan⁡〖𝑦°〗 )/(1/tan⁡〖𝑥°〗 ) = 1/tan⁡〖𝑦°〗 ×tan⁡〖𝑥°〗/1 = 𝒕𝒂𝒏⁡〖𝒙°〗/𝒕𝒂𝒏⁡〖𝒚°〗 Now, tan x° tan⁡〖𝑥°〗=𝐶𝐷/𝐴𝐶 =𝒂/𝑨𝑪 tan y° tan⁡〖𝑦°〗=𝐶𝐵/𝐴𝐶 =(𝑎 + 𝑎)/𝐴𝐶 =𝟐𝒂/𝑨𝑪 Now, 𝒄𝒐𝒕⁡〖𝒚°〗/𝒄𝒐𝒕⁡〖𝒙°〗 = 𝑡𝑎𝑛⁡〖𝑥°〗/𝑡𝑎𝑛⁡〖𝑦°〗 = (𝑎/𝐴𝐶)/(2𝑎/𝐴𝐶) = 𝑎/𝐴𝐶 × 𝐴𝐶/2𝑎 = 𝑎/2𝑎 = 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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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