Question

(SecA+tanA-1)(secA-tanA+1)=2tanA

Answer 1

SecA+tanA-1)(secA-tanA+1)=2tanA

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Answer 2

Solution:

LHS =

(secA+tanA-1)(secA-tanA+1)

= [secA+(tanA-1)][secA -(tanA-1)]

= (sec²A)-(tanA-1)²

/* By algebraic identity :

(x+y)(x-y) = x²-y² */

= sec²A- (tan²A+1-2tanA)

/* By algebraic identity:

(x-y)² = x²+y²-2xy */

= sec²A-tan²A-1+2tanA

= 1-1+2tanA

/* By Trigonometric identity:

sec²A - tan²A = 1 */

= 2tanA

= RHS

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