Question

Prove that tanA/1-cotA+ cotA/1-tanA = tanA + cotA +1

Answer 1

LHS=tanA/1-cotA+1/tanA(1-tanA)
=tansquare A/tanA-1+1/tanA(1-tanA)

CHANGING POSITION OF TERMS WITH SIGN,

1/tanA(1-tanA)-tansquareA/1-tanA

COMMON DENOMINATOR tanA(1-tanA)
1-tancubeA/tanA(1-tanA)
FACTORISING 1-tancubeA=(1-tanA)(1+tansquareA+tanA)
ELIMINATING (1-tanA) FROM BOTH NUMERATOR &DENOMINATOR,
1+tansquareA+tanA/tanA=cotA+tanA+1=RHS