Question

sec A (1-sinA) (sec A + tanA)=1​

Answer 1

Answer

[L.H.S]

$sec A (1-sinA) (sec A + tanA) = 1$

=> $(1/CosA) (1-SinA) (1/CosA + SinA/CosA)$

=> $(1-SinA/CosA) (1+SinA/CosA)$

=> $(1- SinA) (1+SinA)/ Cos^2A$

=> $1-Sin^2A/Cos^2A$       {∵ (a+b)(a-b) = a²-  b² }

=>  $Cos^2A/Cos^2A$       { ∵  1- Sin²A =   Cos²A }

=>  1  [R.H.S]