Question

prove that LHS is equal to RHS

Answer 1

√(1 + sin∅)/√(1 - sin∅)
= √(1 + sin∅) × √(1 + sin∅)/√(1 -sin∅)×√(1 +sin∅)
= √(1 + sin∅)²/√(1 -sin²∅)
= (1 + sin∅)/√cos²∅
= (1 + sin∅)/cos∅
= 1/cos∅ + sin∅/cos∅
= sec∅ + tan∅
hence lhs=rhs

Answer 2

√1+sinA/1-sinA= secA+tanA

LHS,

√(1+sinA)(1+sinA)/(1-sinA) (1+sinA)

=√(1+sinA)²/1-sin²A

=1+sinA/cosA

=1/cosA+sinA/cosA

=secA+tanA

=RHS

proved RHS = LHS