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What is the value of (tan ๐œƒ cosec ๐œƒ) 2 ย  โˆ’ (sin ๐œƒย  sec ๐œƒ)2

(a) โˆ’1 ย  (b) 0 ย  (c) 1 ย  (d) 2

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Question 32 What is the value of (tan ๐œƒ cosec ๐œƒ)2 โˆ’ (sin ๐œƒ sec ๐œƒ)2 (a) โˆ’1 (b) 0 (c) 1 (d) 2 (tan ๐œƒ cosec ๐œƒ)2 โˆ’ (sin ๐œƒ sec ๐œƒ)2 = (sinโกฮธ/cosโกใ€–ฮธ ใ€— ร—1/sinโกใ€–ฮธ ใ€— )^2 โˆ’ (sinโกใ€–ฮธ ใ€—ร—1/cosโกใ€–ฮธ ใ€— )^2 = (1/cosโกใ€–ฮธ ใ€— )^2 โˆ’ (sinโกใ€–ฮธ ใ€—/cosโกใ€–ฮธ ใ€— )^2 = ใ€–๐ฌ๐ž๐œใ€—^๐Ÿ ๐œฝ โˆ’ใ€–๐ญ๐š๐งใ€—^๐Ÿ ๐œฝ = 1 So, the correct answer is (c) We know that 1 + tan2 ฮธ = sec2 ฮธ 1 = sec2 ฮธ โˆ’ tan2 ฮธ sec2 ฮธ โˆ’ tan2 ฮธ = 1

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.