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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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Ex 8.3, 2 Write all the other trigonometric ratios of โˆ  A in terms of sec A. cos A We know that cos A = ๐Ÿ/๐’”๐’†๐’„โก๐‘จ tan A We know that 1 + tan2 A = sec2 A tan2 A = sec2 A โˆ’ 1 tan A = ยฑ โˆš(๐‘ ๐‘’๐‘2 ๐ด โˆ’1) Here, A is acute angle (i.e. less than 90ยฐ) & tan A is positive when A is acute โˆด tan A = โˆš(๐’”๐’†๐’„๐Ÿ ๐‘จ โˆ’๐Ÿ) & tan A is positive when A is acute โˆด tan A = โˆš(๐’”๐’†๐’„๐Ÿ ๐‘จ โˆ’๐Ÿ) cot A cot A = 1/(๐‘ก๐‘Ž๐‘› ๐ด) Putting value of tan A found above = ๐Ÿ/(โˆš(ใ€–๐ฌ๐ž๐œใ€—^๐Ÿโกใ€– ๐‘จ โˆ’๐Ÿใ€— ) ) cosec A We know that 1 + cot2 A = cosec2 A cosec2 A = 1 + cot2 A Putting value of cot A = ๐Ÿ/(โˆš(ใ€–๐’”๐’†๐’„ใ€—^๐Ÿโกใ€– ๐‘จ โˆ’๐Ÿใ€— ) ) cosec2 A = 1 + (1/(โˆš(sec^2โกใ€–๐ด โˆ’ 1ใ€— ) ))^2 cosec2 A = 1 + (1/(๐‘ ๐‘’๐‘2 ๐ด โˆ’ 1)) cosec2 A = ((1 ร— (๐‘ ๐‘’๐‘2 ๐ด โˆ’ 1) + 1)/(๐‘ ๐‘’๐‘2 ๐ด โˆ’1)) cosec2 A = (( ๐‘ ๐‘’๐‘2 ๐ด โˆ’ 1 + 1)/(๐‘ ๐‘’๐‘2 ๐ด โˆ’ 1)) cosec2 A = ( ๐‘ ๐‘’๐‘2 ๐ด )/(๐‘ ๐‘’๐‘2 ๐ด โˆ’ 1) cosec A = ยฑ โˆš(( ๐‘ ๐‘’๐‘2 ๐ด )/(๐‘ ๐‘’๐‘2 ๐ด โˆ’ 1)) cosec A = ยฑ secโก๐ด/โˆš(๐‘ ๐‘’๐‘2 ๐ด โˆ’ 1 ) Here, A is acute angle(i.e. less than 90ยฐ) & cosec A is positive when A is acute โˆด cosec A = secโก๐ด/โˆš(๐‘ ๐‘’๐‘2 ๐ด โˆ’ 1 ) sin A We know that sin A = 1/(๐‘๐‘œ๐‘ ๐‘’๐‘ ๐ด) Putting value of cosec A from above = 1/((secโก๐ด/โˆš(sec^2โกใ€–๐ด โˆ’1ใ€— )) ) = โˆš(๐’”๐’†๐’„๐Ÿ ๐‘จ โˆ’ ๐Ÿ)/๐’”๐’†๐’„โก๐‘จ

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Davneet Singh

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.