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In the given figure, D is the mid-point of BC, then the value of cot 𝑦 Β° cot π‘₯ Β° is

(a) 2 Β  (b) 1/2Β  (c) 1/3Β  (d) 1/4

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Question 32 In the given figure, D is the mid-point of BC, then the value of cot 𝑦 Β° cot π‘₯ Β° is (a) 2 (b) 1/2 (c) 1/3 (d) 1/4 Since D is mid-point of BC Let CD = BD = a Now, π’„π’π’•β‘γ€–π’šΒ°γ€—/𝒄𝒐𝒕⁑〖𝒙°〗 = (1/tan⁑〖𝑦°〗 )/(1/tan⁑〖π‘₯Β°γ€— ) = 1/tan⁑〖𝑦°〗 Γ—tan⁑〖π‘₯Β°γ€—/1 = 𝒕𝒂𝒏⁑〖𝒙°〗/π’•π’‚π’β‘γ€–π’šΒ°γ€— Now, tan xΒ° tan⁑〖π‘₯Β°γ€—=𝐢𝐷/𝐴𝐢 =𝒂/𝑨π‘ͺ tan yΒ° tan⁑〖𝑦°〗=𝐢𝐡/𝐴𝐢 =(π‘Ž + π‘Ž)/𝐴𝐢 =πŸπ’‚/𝑨π‘ͺ Now, π’„π’π’•β‘γ€–π’šΒ°γ€—/𝒄𝒐𝒕⁑〖𝒙°〗 = π‘‘π‘Žπ‘›β‘γ€–π‘₯Β°γ€—/π‘‘π‘Žπ‘›β‘γ€–π‘¦Β°γ€— = (π‘Ž/𝐴𝐢)/(2π‘Ž/𝐴𝐢) = π‘Ž/𝐴𝐢 Γ— 𝐴𝐢/2π‘Ž = π‘Ž/2π‘Ž = 𝟏/𝟐 So, the correct answer is (b)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.