Question

sinA-cosA+1 ÷sinA + cosA-1=cosA÷1-sinA

Answer 1

Hey


Sin∅ - Cos∅ + 1 / Sin∅ + Cos∅ - 1

=( Sin∅ + 1 - Cos∅ )( Sin∅ + 1 + Cos∅ )

divided by

( sin∅ + Cos∅ - 1 ) ( Sin∅ + Cos∅ + 1 )

NoTe :- Here we multiplied the numerator and denominator by same term .


= ( Sin∅ + 1 )² - Cos²∅/ ( Sin∅ + Cos∅)² -1

= Sin²∅ + 1 + 2Sin∅ - Cos²∅ / Sin²∅ + Cos²∅ + 2Sin∅.Cos∅ - 1


= Sin²∅ + 2Sin∅ + ( 1 - Cos²∅ ) / ( Sin²∅ + Cos²∅ ) + 2Sin∅ Cos∅ - 1


= Sin²∅ + 2Sin∅ + Sin²∅ / 1 - 1 + 2Sin∅Cos∅


= 2Sin²∅ + 2Sin∅ / 2Sin∅ . Cos∅


= 2 Sin∅ ( Sin∅ + 1 ) / 2Sin∅ .Cos∅


= Sin∅ + 1 / Cos∅


thanks :)