Question

1+tanAtanA/2=tanA×cotA/2-1=secA

Answer 1

6 answers · Mathematics 

 Best Answer

... LHS 

= 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