The expression can be written as

Question

tanA/1-cotA+cotA/1-tanA can be written as

Answer 1

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