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


Transcript

Ex 8.1, 7 If cot ฮธ = 7/8 , evaluate : (i) ((1 + ๐‘ ๐‘–๐‘›โก๐œƒ)(1 โˆ’ ๐‘ ๐‘–๐‘›โก๐œƒ))/((1 + ๐‘๐‘œ๐‘ โก๐œƒ)(1 โˆ’ ๐‘๐‘œ๐‘ โก๐œƒ)) We will first calculate the value of sin ฮธ & cos ฮธ Now, tan ฮธ = 1/cotโก๐œƒ tan ๐›‰ = ๐Ÿ–/๐Ÿ• We can write tan ๐œƒ = 8/7 (๐’”๐’Š๐’…๐’† ๐’๐’‘๐’‘๐’๐’”๐’Š๐’•๐’† โˆ ๐œฝ)/(๐’”๐’Š๐’…๐’† ๐’‚๐’…๐’‹๐’‚๐’„๐’†๐’๐’• โˆ ๐œฝ)=๐Ÿ–/๐Ÿ• ๐ต๐ถ/๐ด๐ต=8/7 Let BC = 8x & AB = 7x We find AC using Pythagoras Theorem In right triangle ABC Using Pythagoras theorem Hypotenuse2 = Height2 + Base2 AC2 = AB2 + BC2 AC2 = (7x)2 + (8x)2 AC2 = 49x2 + 64x2 AC2 = 113x2 AC = โˆš113๐‘ฅ2 AC = โˆš๐Ÿ๐Ÿ๐Ÿ‘ x AC = โˆš๐Ÿ๐Ÿ๐Ÿ‘ x Now, we need to find sin ฮธ and cos ฮธ sin ๐œฝ = (๐‘ ๐‘–๐‘‘๐‘’ ๐‘œ๐‘๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘’ ๐‘ก๐‘œ โˆ ๐œƒ)/๐ป๐‘ฆ๐‘๐‘œ๐‘ก๐‘’๐‘›๐‘ข๐‘ ๐‘’ = ๐ต๐ถ/๐ด๐ถ = 8๐‘ฅ/(โˆš113 ๐‘ฅ) = ๐Ÿ–/(โˆš๐Ÿ๐Ÿ๐Ÿ‘ ) cos ๐œฝ = (๐‘ ๐‘–๐‘‘๐‘’ ๐‘Ž๐‘‘๐‘—๐‘Ž๐‘๐‘’๐‘›๐‘ก ๐‘ก๐‘œ โˆ ๐œƒ)/๐ป๐‘ฆ๐‘๐‘œ๐‘ก๐‘’๐‘›๐‘ข๐‘ ๐‘’ = ๐ด๐ต/๐ด๐ถ = 7๐‘ฅ/(โˆš113 ๐‘ฅ) = ๐Ÿ•/(โˆš๐Ÿ๐Ÿ๐Ÿ‘ ) We have to find ((๐Ÿ + ๐ฌ๐ข๐งโก๐œฝ ) (๐Ÿ โˆ’ใ€– ๐ฌ๐ข๐งใ€—โก๐œฝ ))/((๐Ÿ + ๐œ๐จ๐ฌโก๐œฝ ) (๐Ÿ โˆ’ใ€– ๐œ๐จ๐ฌใ€—โก๐œฝ ) ) Using (a + b) (a โ€“ b) = a2 โ€“ b2 = ( (12 โˆ’ ๐‘ ๐‘–๐‘›2 ๐œƒ))/( (12 โˆ’ ๐‘๐‘œ๐‘ 2๐œƒ)) = ( (1 โˆ’ ๐‘ ๐‘–๐‘›2 ๐œƒ))/( (1 โˆ’ ๐‘๐‘œ๐‘ 2๐œƒ)) Putting sin ๐œฝ = ๐Ÿ–/(โˆš๐Ÿ๐Ÿ๐Ÿ‘ ) & cos ฮธ = ๐Ÿ•/(โˆš๐Ÿ๐Ÿ๐Ÿ‘ ) = ((1 โˆ’ (8/(โˆš113 ))^2 ))/((1 โˆ’ (7/(โˆš113 ))^2 ) ) = ((๐Ÿ โˆ’ ๐Ÿ”๐Ÿ’/๐Ÿ๐Ÿ๐Ÿ‘))/((๐Ÿ โˆ’ ๐Ÿ’๐Ÿ—/๐Ÿ๐Ÿ๐Ÿ‘) ) = (((113 โˆ’ 64)/113))/(((113 โˆ’ 49)/113) ) = (113 โˆ’ 64)/(113 โˆ’ 49 ) = ๐Ÿ’๐Ÿ—/(๐Ÿ”๐Ÿ’ ) Hence, ((๐Ÿ + ๐’”๐’Š๐’โก๐œฝ)(๐Ÿ โˆ’ ๐’”๐’Š๐’โก๐œฝ))/((๐Ÿ + ๐’„๐’๐’”โก๐œฝ)(๐Ÿ โˆ’ ๐’„๐’๐’”โก๐œฝ)) = ๐Ÿ’๐Ÿ—/(๐Ÿ”๐Ÿ’ ) Ex 8.1, 7 If cot ฮธ = 7/8 , evaluate : (ii) cot2 ฮธ Given cot ฮธ = 7/8 So, cot2 ฮธ = (7/8)^2 = 72/82 = ๐Ÿ’๐Ÿ—/๐Ÿ”๐Ÿ’

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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.