In the given figure, D is the mid-point of BC, then the value of cot π¦ ° cot π₯ ° is
(a) 2 (b) 1/2 (c) 1/3 (d) 1/4
CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ]
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CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ]
Last updated at April 16, 2024 by Teachoo
Question 32 In the given figure, D is the mid-point of BC, then the value of cot π¦ 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, πππβ‘γπΒ°γ/πππβ‘γπΒ°γ = (1/tanβ‘γπ¦Β°γ )/(1/tanβ‘γπ₯Β°γ ) = 1/tanβ‘γπ¦Β°γ Γtanβ‘γπ₯Β°γ/1 = πππβ‘γπΒ°γ/πππβ‘γπΒ°γ Now, tan xΒ° tanβ‘γπ₯Β°γ=πΆπ·/π΄πΆ =π/π¨πͺ tan yΒ° tanβ‘γπ¦Β°γ=πΆπ΅/π΄πΆ =(π + π)/π΄πΆ =ππ/π¨πͺ Now, πππβ‘γπΒ°γ/πππβ‘γπΒ°γ = π‘ππβ‘γπ₯Β°γ/π‘ππβ‘γπ¦Β°γ = (π/π΄πΆ)/(2π/π΄πΆ) = π/π΄πΆ Γ π΄πΆ/2π = π/2π = π/π So, the correct answer is (b)