Question

please solve this. ....please

Answer 1

L.H.S = (Cosec A - Sin A) (Sec A - Cos A)

= (Cosec A - 1/Cosec A ) (Sec A  -  1/Sec A)

= (Cosec ^2 A -1 / Cosec A)  (Sec ^2 A -1/ Sec A)

= (Cot^2 A / Cosec A )  (Tan^2 A/ Sec A)

= (Cos^2 A /Sin^2 A* Sin A)  ( Sin^2 A/Cos^2 A*Cos A)

= (Cos^2 A/Sin A* Sin^2 A/CosA)

= Cos A . Sin A

R.H.S

= 1 / (Tan A + Cot A)

= 1 / ( Sin A /Cos A + Cos /Sin A)

= 1 / [ (Sin^2A + Cos^2A/Sin A Cos A]

=  1 / ( 1 / Sin A Cos A)

=  Sin A Cos A

L.H.S = R.H.S  (PROVED)