Question

(secx-tanx)(secx+tanx)=1 simplify

Answer 1

Explanation:

(secx-tanx)(secx+tanx)

=sec^2-tan^2

=1

Answer 2

Explanation:

LHS = (sec x - tan x)(Sec x - tan x)

= sec² x - tan²x {(a +b)(a-b) = a² - b²}

`= (1)/(Cos^(2) \ x)-(Sin^(2) \ x)/(Cos^(2) \ x)\\\\\\= (1-Sin^(2) \ x)/(Cos^(2) \ x)\\\\= (Cos^(2) \ x)/(Cos^(2) \x)\\\\= 1`

Hence proved.