Question

How do you verify `sec(x+y)= (secx secy)/(1-tanxtany)`?

Answer 1

Verify `(sec x.sec y)/(1 - tan x.tan y) = sec (x + y)`

Explanation:

`((1/cos x)(1/cos y))/((1 - (sin x.sin y)/(cos x.cos y))` =

= `1/(cos x.cos y - sin x.sin y) = 1/cos (x + y) =` `sec (x + y)`

Answer 2

Let us start with, x = `30^0` = y.
we shall show that both left hand side and right hand side equal in value to 2

Explanation:

L.H.S. = sec ( `30^0` + `30^0`) = `sec 60 ^0` = 2 .. (1)
R.H.S. = sec`30^0`sec`30^0` / [1 - `tan 30^0 tan 30^0`]
= (2 / `sqrt 3`)(2 / `sqrt 3`) / [ 1 - (1/`sqrt3` )(1/`sqrt3` )]
= (4/3) / {1 - 1/3}
= (4/3)x(3/2)
= 2 ....(2)
From (1) and (2) LHS = RHS.
Hence the verification is complete.