Question

sin A + cos A/ sinA- cos A + sin A - cos / sin A+ cos A =2 / sin A square A - cos A square= 2/2 sin square A -1= 2/1-2cos A square​

Answer 1

LHS =

( sinA+cosA). ( sinA - cosA)

----------------------- + ----------------------

( sinA - cosA) ( sinA+ cosA)

( sinA+ cosA)²+ ( sinA - cosA)²

= ------------------------------------------------

( sin²A - cos²A)

2( sin²A + cos²A)

= ------------------------------------

( sin²A - cos²A)

2

= --------------------------- = middle term (1)

( sin²A - cos²A)

2

= ------------------------------

[ sin²A-(1- sin²A) ]

2

= ------------------. = middle term (2)

2sin²A-1

2

= -----------------------------

[ 2(1- cos²A) -1]

2

=. ----------------------

1 - 2 cos²A

= RHS

Hence proved

hope this helps you