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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Example 11 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) = (𝒄𝒐𝒔𝒆𝒄 𝑨 βˆ’ 𝟏)/(𝒄𝒐𝒔𝒆𝒄 𝑨 + 𝟏) = R.H.S. So, L.H.S = R.H.S Hence proved

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Davneet Singh

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.