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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 You are here
Misc. 6 Deleted for CBSE Board 2023 Exams
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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 May 12, 2021 by Teachoo
Misc 5 Prove cos-1 4/5 + cos-1 12/13 = cos-1 33/65 Let a = cos-1 4/5 and b = cos-1 12/13 Finding sin a, cos a Let a = cos-1 4/5 cos a = 4/5 We know that sin a = β(1 βcos^2β‘π ) =β(1β(4/5)^2 ) " =" β(9/25) "=" 3/5 We use cos (a + b) formula Finding sin b, cos b Let b = cos-1 12/13 cos b = 12/13 We know that sin b = β(1 βπππ 2 π) = β(1 β(12/13)^2 ) = β(25/169) = 5/13 Now, cos (a + b) = cos a cos b β sin a sin b cos (a + b) = 4/5 Γ 12/13 β 3/5 Γ 5/13 = 48/65 β 3/13 = (48 β 3(5))/65 = (48 β 15)/65 = ππ/ππ Putting cos a = 4/5 , sin a = 3/5 & cos b = 12/13 , sin b = 5/13 Thus, cos (a + b) = 33/65 a + b = cos-1 (33/65) Putting a = cos-1 4/5 & b = cos-1 12/15 cos-1 π/π + cos-1 ππ/ππ = cos-1 ππ/ππ Which is what we had to prove Hence proved