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Ex 3.3, 8 - Prove cos (pi + x) ... - Chapter 3 Class 11 Trigonometry

Ex 3.3, 8 - Chapter 3 Class 11 Trigonometric Functions - Part 2

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Ex 3.3, 8 Prove that cos⁑〖 (Ο€ + π‘₯) cos⁑〖(βˆ’ π‘₯)γ€— γ€—/(sin⁑〖 (Ο€ βˆ’ π‘₯)γ€— cos⁑〖"(" Ο€/2 " + " π‘₯")" γ€— ) = cot2 π‘₯ Taking L.H.S. π‘π‘œπ‘ β‘γ€–(πœ‹ + π‘₯) γ€–π‘π‘œπ‘  〗⁑〖(βˆ’π‘₯)γ€— γ€—/(𝑠𝑖𝑛⁑(πœ‹ βˆ’ π‘₯) π‘π‘œπ‘ β‘γ€–"(" πœ‹/2 " + " π‘₯")" γ€— ) Putting Ο€ = 180Β° = π‘π‘œπ‘ β‘γ€–(180Β° + π‘₯) γ€–π‘π‘œπ‘  〗⁑〖(βˆ’π‘₯)γ€— γ€—/(𝑠𝑖𝑛⁑(180Β° βˆ’ π‘₯) π‘π‘œπ‘ β‘γ€–"(" 90Β° "+ " π‘₯")" γ€— ) Using cos (180Β° + x) = –cos x cos (βˆ’x) = cos x sin (180Β° – x) = sin x & cos(90Β° + x) = –sin x = (βˆ’π‘π‘œπ‘ β‘γ€–π‘₯ Γ— π‘π‘œπ‘ β‘π‘₯ γ€—)/((sin⁑〖π‘₯) Γ—γ€–(βˆ’sin〗⁑π‘₯) γ€— ) = (βˆ’π‘π‘œπ‘ 2π‘₯)/(βˆ’π‘ π‘–π‘›2π‘₯) = cot2x = R.H.S. Hence proved

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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.