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Miscellaneous
Misc. 2 Important
Misc. 3 Deleted for CBSE Board 2023 Exams
Misc. 4 Important Deleted for CBSE Board 2023 Exams
Misc. 5 Deleted for CBSE Board 2023 Exams
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Misc. 7 Important Deleted for CBSE Board 2023 Exams
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Misc. 10 Important Deleted for CBSE Board 2023 Exams
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Misc 12 Important Deleted for CBSE Board 2023 Exams
Misc. 13 Important Deleted for CBSE Board 2023 Exams
Misc. 14 Deleted for CBSE Board 2023 Exams
Misc 15 (MCQ) Important Deleted for CBSE Board 2023 Exams
Misc 16 (MCQ) Important Deleted for CBSE Board 2023 Exams
Misc 17 (MCQ) Deleted for CBSE Board 2023 Exams
Miscellaneous
Last updated at March 22, 2023 by Teachoo
Misc 8 Prove that tanโ1 1/5 + tanโ1 1/7 + tanโ1 1/3 + tanโ1 1/8 = ๐/4 We know that tanโ1 x + tanโ1 y = tanโ1 ((๐ฑ + ๐ฒ )/(๐ โ ๐ฑ๐ฒ)) tanโ1 ๐/๐ + tanโ1 ๐/๐ = tanโ1 (1/5 + 1/7)/(1โ 1/5 ร 1/7) = tanโ1 ((7 + 5)/(5(7)))/( (35 โ 1)/35 ) = tanโ1 (6/17) tanโ1 ๐/๐ + tanโ1 ๐/๐ = tanโ1 (1/3 + 1/8)/(1โ 1/3 ร 1/8) = tanโ1 ( (8 + 3)/(3(8)))/( (24 โ 1)/24) = tan โ 1 (11/23) Solving L.H.S tanโ1 1/5 + tanโ1 1/7 + tanโ1 1/3 + tanโ1 1/8 = ("tanโ1 " 1/5 " + tanโ1 " 1/7) + ("tanโ1 " 1/3 " + tanโ1 " 1/8) = tan-1 (๐/๐๐) + tanโ1 (๐๐/๐๐) = tanโ1 (6/17 + 11/23)/(1 โ 6/17 ร 11/23) We know that tanโ1 x + tanโ1 y = tanโ1 ((๐ + ๐ )/(๐ โ ๐๐)) Replacing x by 6/17 and y by 11/23 = tanโ1 ( (6(23) + 11(17))/(17(23)))/(1 โ 66/391) = tanโ1 ( (138 + 187)/391)/((391 โ 66)/391) = tanโ1 ( 325/391)/(325/391) = tanโ1 1 = tanโ1 ("tan " ๐ /๐) = ฯ/4 = R.H.S Hence proved (As tan ๐/4 = 1)