Question

Cos theta - sin theta + 1/ cos theta + sin theta - 1 = ?​

Answer 1

Giventhat,

cosθ+sinθ−1

cosθ−sinθ+1

=cosecθ+cotθ

Now,

DividebothN

r

andD

r

withsinθ

=

sinθ

cosθ+sinθ−1

sinθ

cosθ−sinθ+1

=

cotθ+1−cosecθ

cotθ−1+cosecθ

=

cotθ−cosecθ+1

cotθ+cosecθ−(cosec

2

θ−cot

2

θ)

=

cotθ−cosecθ+1

cotθ+cosecθ−cosec

2

θ+cot

2

θ

=

cotθ−cosecθ+1

cotθ+cosecθ(1−(cosec

2

θ−cot

2

θ))

=cotθ+cosecθ

HenceL.H.S=R.H.S