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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

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.