**The above expression can be written as secA.cosecA+1**

**Proof:**

Writing tan as sin/cos and cot as cos/sin,

LHS = [ (sin/cos) / ( 1 - cos/sin ) ] + [ ( cos/sin ) / ( 1 - sin/cos ) ]

...... = [ sin² / ( cos(sin-cos) ) ] + [ cos² / ( sin(cos-sin) ) ]

...... = ( sin³ - cos³ ) / [ sincos(sin-cos) ]

...... = ( sin-cos ) ( sin² + sincos + cos² ) / [ sincos(sin-cos) ]

...... = ( 1 + sincos ) / ( sincos )

...... = ( 1 / sincos ) + ( sincos / sincos )

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

...... = sec. cosec + 1

...... = RHS