Question

(sinX+cosX)(tanX+cotX)=secX+cosecX prove both are equal

Answer 1

↑Above is the required answer.
Note: I used A instead of X.

Answer 2

Hi friend,

Here is your answer,
_____________________________________________________________

To prove : (sinx+cosx)(tanx+cotx) = secx+cosecx

LHS = (sinx+cosx)( sinx   + cosx )
                               cosx      sinx

        = (sinx+cosx )(sin²x+cos²x)
                               (cosx.sinx)

        = (sinx+cosx)(     1       )
                             (cosx.sinx)

        = (sinx+cosx)
            cosx.sinx
        =         sinx          +          cosx         
             cosx.sinx              cosx.sinx
        = ¹/cosx + ¹/sinx
        = secx + cosecx
        =  RHS

Hence Proved.
_____________________________________________________________

★★★★ HOPE THIS HELPS YOU ★★★★
★★★★ PLS MARK ME AS BRAINLIEST ★★★★