Ex 3.3, 8 - Chapter 3 Class 11 Trigonometric Functions (Important Question)

Last updated at April 16, 2024 by

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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‘₯ Solving L.H.S. 𝒄𝒐𝒔⁑〖(𝝅 + 𝒙) 〖𝒄𝒐𝒔 〗⁑〖(βˆ’π’™)γ€— γ€—/(π’”π’Šπ’β‘(𝝅 βˆ’ 𝒙) 𝒄𝒐𝒔⁑〖"(" 𝝅/𝟐 " + " 𝒙")" 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’π’”β‘γ€–π’™ Γ— 𝒄𝒐𝒔⁑𝒙 γ€—)/((π’”π’Šπ’β‘γ€–π’™) Γ—γ€–(βˆ’π’”π’Šπ’γ€—β‘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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.