Question

sinA (1 + tanA)² + cosA (1 + cotA) = secA + cosecA

Answer 1

Correction :

sin A ( 1 + tan A ) + cos A ( 1 + cot A ) = sec A + cosec A

L.H.S

= sin A + sin A tan A + cos A + cos A cot A

= sin A + sin²A / cos A + cos A + cos²A/sin A

= sin A + cos²A/sin A + sin²A / cos A + cos A

= ( sin²A + cos²A )/sin A + ( sin²A + cos²A )/cos A

= 1/sin A + 1/cos A

= sec A + cosec A

Hence proved !