Question

prove that sinx(1+tanx)+cosx(1+cotx)=secx+cosecx.pls help me

Answer 1

Answer:

sinx[1 + sinx /cosx ]  + cosx [1+ cosx / sinx ]

now by  simplifying the bracket portion

sinx [ cosx + sinx /cosx ] +cosx [ sinx + cosx / sinx ]

[sinx + cosx] [ sin^2x + cos^2x /sinxcosx ]

now as we know that sin^2x+ cos^2x = 1

so here

now [sinx + cosx ] [ 1 /sinxcosx ]

[sinx  + cosx / sinxcosx]

now taking sinxcosx as a denominator

we got our result as 1 /cosx + 1 / sinx  = secx + cosecx

hernce proved