Question

Tan A + secA=2 find the value of tan square A+ sec Square A

Answer 1

Please find the answer in the attachment.

Answer 2

sec A + tan A = 2 1.
sec^2 A - tan^2 A = 1
( sec A + tan A ) ( sec A - tan A ) = 1
2 ( sec A- tan A ) =1
sec A - tan A = 1/2 2.

eliminating 1 and 2 , we get ,
sec A + tan A = 2
sec A - tan A = 1/2
_______________
2sec A = 5/2
sec a = 5/4

substitute sec A in 1
5/4 + tan A = 2
tan A = 2-5/4
tan A = 8 - 5/4
tan A = 3/4

tan^2 A + sec^2 A = (3/4)^2 + (5/4)^2
= 9/16 + 25/16
= 34/16
= 17/8

hope it helps you!!!!