Question

Prove that-(secA+tanA-1)(secA-tanA+1)=2tanA

Answer 1

{secA+(tanA-1)}{secA-(tanA-1)}=(secA)² - (tanA-1)²
                                                  =sec²A - tan²A - 1 + 2tanA
                                                  =1 - 1 + 2tanA
                                                  =2tanA

Answer 2

We can write the above equation as
{(secA)+(tanA-1)}*{(secA) - (tanA-1)}
It is in the formula (a+b)*(a-b) = a²-b²
So,
=> (secA)² - (tanA-1)²
=> sec²A - [tan²A + 1 - 2tanA]
=> sec²A - tan²A - 1 +2tanA
=> (sec²A - tan²A) - 1 +2tanA ......As sec²A - tan²A = 1
So,
=> 1 - 1 +2tanA
= 2tanA