Question

How do you prove `tanx/secx + cotx/cscx = sinx+cosx`?

Answer 1

`(sin x/cos x).(cos x/1) + (cos x/sin x)(sin x/1) =`
`= sin x + cos x`

Answer 2

See the Proof in Explanation.

Explanation:

`"The L.H.S."=(tanx+cotx)/(secx+cscx)`

`=(sinx/cosx+cosx/sinx)/(1/cosx+1/sinx)`

`={(sin^2x+cos^2x)/cancel((cosxsinx))}/{(sinx+cosx)/cancel((cosxsinx))}`

`=1/(cosx+sinx)`

`="the R.H.S."`