secxtanx cotx cscxcos2 x is this a trig identitySolutiongi

secx(tanx + cotx = cscx/cos^2 x is this a trig identity

given

secx(tanx +cotx) = cscx/cos^2x

to prove take left hand side

LHS = secx(tanx +cotx)

now secx = 1/cosx , tanx = sinx/cosx and cotx = cosx/sinx , plug all these values

L.H.S= 1/cosx ( sinx /cosx + cosx /sinx)

= 1/cosx[ (sin^2 x +cos^2 x) /cosxsinx ]

but sin^2 x +cos^2 x=1

L.H.S= 1/cosx [ 1/ cosxsinx ]

= 1/(cos^2 x sinx)

but 1/sinx = cscx

L.H.S = cscx/cos^2 x

L.H.S=R.H.S

so hence proved