Question

1+tanAtanA/2 =tanA.cotA/2=secA

Answer 1

1 + [ tan A. tan (A/2) ]  

= 1 + [ sin A. sin (A/2) / cos A. cos (A/2) ]  

= [ cos A. cos (A/2) + sin A. sin (A/2) ] / [ cos A. cos (A/2) ]  

= [ cos ( A - (A/2) ) ] / [ cos A. cos (A/2) ]  

= [ cos (A/2) ] / [ cos A. cos (A/2) ]  

= 1 / ( cos A )  

= sec A ........................................... (1)  

.........................................  

... RHS  

= [ tan A. cot (A/2) ] - 1  

= [ sin A. cos (A/2) / cos A. sin (A/2) ] - 1  

= { [ sin A. cos (A/2) - cos A. sin (A/2) ] / [ cos A. sin (A/2) ] }  

= { [ sin ( A - A/2 ) ] / [ cos A. sin (A/2) ] }  

= [ sin (A/2) ] / [ cos A. sin (A/2) ]  

= 1 / ( cos A )  

= sec A