Question
Verify the identity.
cos x - sec x = -sin x tan x
So far I have applied a reciprocal identity
=cos x - 1/cos x
I know I must combine using the least common denominator but I don't know how it would be written.
cos x - sec x = -sin x tan x
So far I have applied a reciprocal identity
=cos x - 1/cos x
I know I must combine using the least common denominator but I don't know how it would be written.
Answers
Scott
multiplying by cosine
... cos^2(x) - 1 = sin^2(x)
... cos^2(x) - 1 = sin^2(x)
Reiny
To prove an identity, we usually start with one side and using basic identities show that it is equal to the other side
LS = cosx - sex
= cosx - 1/cosx
= (cos^2 x - 1)/cosx
= - sin^2 x / cosx
= -sinx(sinx/cosx)
= -sinx tanx
= RS
LS = cosx - sex
= cosx - 1/cosx
= (cos^2 x - 1)/cosx
= - sin^2 x / cosx
= -sinx(sinx/cosx)
= -sinx tanx
= RS