(1+tanx)/(sinx + cosx) = secx
please help this is so hard
2007-02-04 17:20:13 · 3 answers · asked by ARB 2 in Science & Mathematics ➔ Physics
oops wrong category
2007-02-04 17:21:58 · update #1
Not too hard.
(1 + tan x) / (sin x + cos x)
= (1 + sin x / cos x) / (sin x + cos x)
= [(cos x + sin x) / cos x] / (sin x + cos x)
= [1 / cos x] / 1
= 1 / cos x
= sec x.
2007-02-04 17:24:32 · answer #1 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
tan x can be written as (sin x)/(cos x)
putting this value in the expression
(1 + tan x)\(sin x + cos x)
we get
{1 + (sin x)/(cos x)}/{sin x+cos x}
on taking the LCM of the denominators we get,
{(cos x + sin x)/(cos x)}/{(cos x + sin x)}
The factor (cos x + sin x) is canceled and we have only 1/cos x left ie. sec x.
Left hand side = Right hand side
Hence Proved
2007-02-05 01:31:46 · answer #2 · answered by D 2 · 0⤊ 0⤋
Why you put your question in physics column?
2007-02-05 01:22:51 · answer #3 · answered by li mei 3 · 0⤊ 0⤋