Question

prove that CotA+CosecA-1/CotA-CosecA+1 = 1+CosA/SinA.

Answer 1

Hiiii friend,


CotA+CosecA-1/CotA-CosecA+1 = 1+CosA/SinA.

We have,


LHS= CotA+CosecA-1/CotA-CosecA+1


=> CotA+CosecA-(Cosec²A-Cot²A) / CotA-CosecA+1


=> (CotA+CosecA)-(CosecA-CotA)(CosecA+CotA)/ (CotA-CosecA+1)




=> (CotA+CosecA)[(1-(CosecA-CotA)]/ CotA-CosecA+1


=> (CosecA+CotA)[(1-CosecA+CotA)] / (CotA-CosecA+1)

=> (CosecA+CotA)

=> 1/SinA + CosA/SinA

=> 1+CosA/SinA = RHS.

Hence,


LHS = RHS......PROVED.....

HOPE IT WILL HELP YOU..... :-)