Question

Cosec theta/ Cosec theta -1 + Cosec theta/Cosec theta+1 = 2 sec²thta = 2 +2 Tan²Theta

Answer 1

Hiii friend,


Cosec¢/Cosec¢-1 + Cosec¢/Cosec¢+1 = 2 × Sec²¢ = 2+2 Tan²¢


We have,


LHS = (Cosec¢/Cosec¢-1 + Cosec¢/Cosec¢+1)



=> Cosec²¢ + Cosec¢ + Cosec²¢ - Cosec¢/(Cosec¢-1)(Cosec¢+1)


=> 2 × Cosec²¢/ Cosec²¢ -1


=> 2 Cosec²¢/Cot²¢

=> (2/Sin²¢ / Cos²¢/Sin²¢)


=> 2/Cos²¢ = 2 Sec²¢


=> 2 Sec²¢ = 2(1+Tan²¢)


=> 2 + 2 Tan²¢ = RHS


Hence,


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

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