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

2 Answers
Jul 20, 2015

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)

Jul 20, 2015

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. = sec30^0sec30^0 / [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.