Question

prove that( Sin A /1+ cosA +1+cos A/sinA) ( cosA/1 + sinA + 1 + sin A/cos A) = 4 secA. cosecA​

Answer 1

Here is the solution -

=(sinA + 1 - cosA) / (cosA - 1 + sinA)

Divide each term by cosA

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

=[tanA + secA - ( )] /

( 1 - secA + tanA)

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

= tanA + secA

= (sinA / cosA )+ 1 / cosA

= (sinA + 1 )/ cosA

Hence Proved