Question

(secx-secy)/(tanx+tany)+(tany-tanx)/(secx+secy)
=?​

Answer 1

Step-by-step explanation:

The simplified value of (secx secy+tanx tany)2−(secx tany tanx secy)2 is

A) -1

B) 0

C) sec2x

D) 1

Correct Answer:

D) 1

Description for Correct answer:

(sec x.sec y+tan x.tan y)2−(sec x.tan y+tan x.sec y)2

=(sec2x.sec2y+tan2x.tan2y+2sec x.sec y.tan x.tan y)

−(sec2x.tan2+tan2x.sec2y+2secx.secy.tanx.tany)

=sec2x.sec2y+tan2x.tan2y−sec2x.tan2y−tan2x.sec2y

=sec2x.sec2y−sec2x.tan2y

−tan2x.sec2y+tan2x.tan2y

=sec2x(sec2y−tan2y)

−tan2x(sec2y−tan2y)

=sec2x−tan2x=1