. Solve(1+cotA-cosecA)(1+tanA+secA)=2

Best Answer

Explanation:

LHS = (1 + cot A - cosec A)(1+ tan A + sec A)

= (1 + Cos ASin A - 1Sin A) (1+ Sin ACos A - 1Cos A)

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

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

= (Sin A + Cos A)2 - (1)2 Sin A Cos A

= (Sin 2A + Cos 2A + 2 Sin A Cos A  - 1 Sin A Cos A

= ( 1 + 2 Sin A Cos A  - 1 )Sin A Cos

= 2 Sin A Cos A Sin A Cos A=2

Final Answer:

Hence, we get  2, as the answer.