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


Transcript

Prove the following identities, where the angles involved are acute angles for which the expressions are defined. ((1 +π‘‘π‘Žπ‘›2 𝐴)/(1 + π‘π‘œπ‘‘2 𝐴))=((1 βˆ’tan⁑〖 𝐴〗)/(1 βˆ’cot⁑ 𝐴))^2=π‘‘π‘Žπ‘›2 𝐴 Solving ((𝟏 + π’•π’‚π’πŸ 𝑨)/(𝟏 + π’„π’π’•πŸ 𝑨)) ((1 + π‘‘π‘Žπ‘›2 𝐴)/(1 + π’„π’π’•πŸ 𝐴)) = ((1 + π‘‘π‘Žπ‘›2 𝐴))/(((1+ 𝟏/(π’•π’‚π’πŸ 𝑨)) ) = ((1 + π‘‘π‘Žπ‘›2 𝐴))/(((tan^2⁑𝐴 + 1))/(tan^2⁑𝐴 ))= (π‘‘π‘Žπ‘›2 𝐴 (1 + π‘‘π‘Žπ‘›2 𝐴))/((π‘‘π‘Žπ‘›2 𝐴 + 1)) = tan2 A = R.H.S Solving ((πŸβˆ’ 𝒕𝒂𝒏⁑𝑨)/(πŸβˆ’ 𝒄𝒐𝒕⁑𝑨 ))^𝟐 ((1βˆ’ tan⁑𝐴)/(1βˆ’ 𝒄𝒐𝒕⁑𝑨 ))^2 = ((1 βˆ’ tan⁑〖 𝐴〗)/(1 βˆ’ 𝟏/𝒕𝒂𝒏⁑〖 𝑨〗 ) " " )^2 = (((1 βˆ’ tan⁑〖 𝐴)γ€—)/(((tan⁑〖 𝐴 βˆ’1γ€— ))/tan⁑〖 𝐴〗 ))^2 = (tan⁑〖 𝐴(1 βˆ’ tan⁑〖 𝐴)γ€— γ€—/( (tan⁑〖 𝐴 βˆ’1)γ€— ))^2 = (tan⁑〖 𝐴(1 βˆ’ tan⁑〖 𝐴)γ€— γ€—/(βˆ’(1 βˆ’ tan⁑〖 𝐴)γ€— ))^2 = (βˆ’tan⁑𝐴 )^2 = tan2 A = RHS Therefore, ((1 + π‘‘π‘Žπ‘›2 𝐴)/(1 + π‘π‘œπ‘‘2 𝐴))=((1 βˆ’ tan⁑〖 𝐴〗)/(1 βˆ’ cot⁑ 𝐴))^2=π‘‘π‘Žπ‘›2 𝐴 H\ence 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.