Question

If cosec θ – sin θ = a , sec – cos = b , find the value of a b ?

Answer 1

cosec θ - sin θ = a

1/sin θ - sin θ = a

( 1 - sin ^2)/sin θ = a

cos ^2 θ / sin θ = a.




sec θ - cos θ = b.

1 / cos θ - cos θ = b.

( 1 - cos ^2 θ ) / cos θ = b.

sin ^2 θ / cos θ = b.


ab = cos ^2 θ/ sin θ * sin ^2 θ / cos θ

= cos θ sin θ.

Answer 2

Hey

a = cosec@ - sin@

a = 1/sin@ - sin@

a = 1 - sin²@ / sin@

a = cos²@ / sin@ ––( i )

And ,

b = sec@ - cos@

b = 1/cos@ - cos@

b = 1 - cos²@ / cos@

b = sin²@ / cos@ ——( ii )

So now ,

ab = cos²@ / sin@ × sin²@ / cosa


ab = cos@ × sin@


So , required answer is cos@ × sin@


thanks :)