Question

sec theta÷sec theta+1+sec theta÷sec theta-1=2 cosec^2 theta​

Answer 1

Step-by-step explanation:

Hi,

Here I am using A instead of theta.

LHS = secA/(secA+1) + secA/(secA-1)

= SecA[ 1/(secA+1) + 1/(secA-1 ) ]

= SecA[ ( secA-1+secA+1 )/(sec² A-1²) ]

= SecA[ 2secA/tan² A ]

= 2sec²A/ tan² A

= ( 2/cos² A ) / ( sin² A/cos² A )

= 2/sin² A

= 2cosec²A

= RHS

I hope this helps you.

:)