Question

prove that cos2A÷1+sin2A=tan (45°-A)

Answer 1

cos2A=(cosA^2-sinA^2)= cosA^2( 1-tanA^2) =1-tanA^2/(secA^2). =1-tanA^2/1+ tanA^2. 1+sin2A= sinA^2+ cosA^2+ 2 sinAcosA. hence 1+sin2A =(sinA+ cosA)^2 = cosA ^2((tanA+1)^2). cos2A/1+sin2A= (1-tanA)(1+tanA)/ (secA^2.cosA^2)(1+tanA)(1+tanA)=(1-tanA)/(1+tanA) hence tan45-tanA/1+ tan45tanA since tan45 is 1 only it can be written as tan(45-A). hence proved . please mark it as brainliest