Example 14 - Prove that cot A - cos A / cot A + cos A - Examples

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  1. Chapter 8 Class 10 Introduction to Trignometry
  2. Serial order wise
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Example 14 Prove that cot⁑〖𝐴 βˆ’ cos⁑𝐴 γ€—/cot⁑〖𝐴 + cos⁑𝐴 γ€— =(π‘π‘œπ‘ π‘’π‘ 𝐴 βˆ’ 1)/(π‘π‘œπ‘ π‘’π‘ 𝐴 + 1) Taking L.H.S cot⁑〖𝐴 βˆ’γ€– cos〗⁑𝐴 γ€—/cot⁑〖𝐴 +γ€– cos〗⁑𝐴 γ€— Writing everything in terms of sin A and cos A = (cos⁑〖 𝐴〗/sin⁑〖 𝐴〗 βˆ’γ€– cos〗⁑〖 𝐴〗)/(cos⁑〖 𝐴〗/sin⁑〖 𝐴〗 +γ€– cos〗⁑〖 𝐴〗 ) = cos⁑〖 𝐴 βˆ’γ€– cos〗⁑〖 𝐴 sin⁑〖 𝐴〗 γ€— γ€—/(sin⁑〖 𝐴〗/(cos⁑〖 𝐴 + cos⁑〖 𝐴 sin⁑〖 𝐴〗 γ€— γ€—/sin⁑〖 𝐴〗 )) = ( (𝒄𝒐𝒔⁑〖 𝑨〗 βˆ’ 𝒄𝒐𝒔⁑〖 𝑨〗 sin⁑〖 𝐴 γ€—))/((𝒄𝒐𝒔⁑〖 𝑨〗 + 𝒄𝒐𝒔⁑〖 𝑨〗 sin⁑〖 𝐴 γ€—)) = (𝒄𝒐𝒔⁑〖 𝑨〗 (1 βˆ’ sin⁑〖 𝐴 γ€—))/(𝒄𝒐𝒔⁑〖 𝑨〗 (1 + sin⁑〖 𝐴 γ€—)) = ( (1 βˆ’ sin⁑〖 𝐴 γ€—))/( (1 + sin⁑〖 𝐴 γ€—)) Dividing sin A on numerator and denominator = ( ((1 βˆ’ sin⁑〖 𝐴 γ€—))/(π’”π’Šπ’ 𝑨))/( ((1 + sin⁑〖 𝐴 γ€—))/(π’”π’Šπ’ 𝑨 )) = ( 1/(𝑠𝑖𝑛 𝐴) βˆ’ (𝑠𝑖𝑛 𝐴)/(𝑠𝑖𝑛 𝐴))/(1/(𝑠𝑖𝑛 𝐴) + (𝑠𝑖𝑛 𝐴)/(𝑠𝑖𝑛 𝐴)) = ( 1/(𝑠𝑖𝑛 𝐴) βˆ’ 1)/(1/(𝑠𝑖𝑛 𝐴) + 1) = (π‘π‘œπ‘ π‘’π‘ 𝐴 βˆ’ 1)/(π‘π‘œπ‘ π‘’π‘ 𝐴 + 1) = R.H.S. So, L.H.S = R.H.S Hence proved

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.