Question

Calvin must prove that this equation is an identity.
tanx=(1/sinxcosx)-(cosx/sinx)

Answer 1

1/(sinxcosx) - cosx/sinx
= 1/(sinxcosx) - cos^2x/(sinxcosx)
= (1-cos^2x)/(sinxcosx)
= sin^2x/(sinxcosx)
= sinx/cosx
= tanx

Answer 2

*where cos^2x + sin^2x = 1 (from trig identities)

Answer 3

\[\tan x = \sin x/\cos x = \sin ^{2}x/(\sin x \cos x) = (1-\cos ^{2}x)/(\cos x \sin x)\]

separating the numerator intor into 2 terms u'll get right hand side part