Question

cos theta*cot theta / 1 + sin theta = cosec theta - 1 ,
Prove

Answer 1

Hi ,

Here I am using A instead of theta.

LHS = cosA cotA/( 1 + sinA )

= [ cosA( cosA/sinA )]/( 1 + sinA )

= ( cos²A )/[ sinA( 1 + sinA ) ]

= ( 1 - sin²A )/[ sinA ( 1 + sinA ) ]

= ( 1 + sinA )( 1 - sinA )/ [ sinA ( 1 + sinA ) ]

after cancellation , we get

= ( 1 - sinA )/sinA

= 1/sinA - sinA/sinA

= Cosec A - 1

= RHS

I hope this helps you.

: )

Answer 2

Hi,

Please see the attached file!


Thanks