28, cos2A = Istana1+ tan2 A

1.	28, cos2A = Istana1+ tan2 A
Answer» 1 - tan^2(A) / 1 + tan^2(A) = cos2A Solving from LHS is easy I guess So LHS = (1 - tan^2 A)/ (1+tan^2 A) = {( 1 - sin^2 A / cos^2 A) } / Sec^2 A = {( Cos^2 A - Sin^2 A)/Cos^2 A } / (Sec^2 A) = { ( Cos^2 A - Sin^2 A)/Cos^2 A } * Cos^2 A = Cos^2 A - Sin^2 A = Cos 2A = RHS ... Hence the proof... Important formulas used : Cos2A = Cos^2 A - Sin^2 A tan^2 A +1 = Sec^2 A Sec^2 A = 1/ Cos^2 A Tan^2 A = Sin^2 A / Cos^2 A

Answer»

1 - tan^2(A) / 1 + tan^2(A) = cos2A

Solving from LHS is easy I guess

LHS = (1 - tan^2 A)/ (1+tan^2 A)

= {( 1 - sin^2 A / cos^2 A) } / Sec^2 A

= {( Cos^2 A - Sin^2 A)/Cos^2 A } / (Sec^2 A)

= { ( Cos^2 A - Sin^2 A)/Cos^2 A } * Cos^2 A

= Cos^2 A - Sin^2 A

= Cos 2A

= RHS ... Hence the proof...

Important formulas used :

Cos2A = Cos^2 A - Sin^2 A

tan^2 A +1 = Sec^2 A

Sec^2 A = 1/ Cos^2 A

Tan^2 A = Sin^2 A / Cos^2 A

Discussion