LHS= tanA+cotA= sinA/cosA +cosA/sinA

                               =    take lcm .then after taking lcm we get  ,( sin²A+cos²A)/sinA.cosA=  1/(sinA.cosA) = 2/2sinAcosA  { multiplying and dividing the numerator by 2}  =2/sin2A =2cosec2A

now we know that  ........    cosec2A is always greater than or equal to 1                       { yes of course always less than -1 also, but we dont need to consider it in this problem}              

 so.......                 cosec2a>or = 1

                               2cosec2A>=2 ..... so here we can say tanA +cotA  is not equal to 3/2 since it has to be greater than or equal to 2.

hence,proved