tanA=5/6 tanB=1/11 prove that A+B=45°

solve the following

tan65° cot165°

tan(a+b)= (tana+tanb)/(1 – tana*tanb)

put values of tanA=5/6 tanB=1/11 to get

tan(a+b)= 1 

tan(a+b)= tan 45

a+b= 45

 

now tan65° cot165°= tan65° cot(180 – 15°)= – tan65° cot15°= – tan65° tan(90 – 15°)

= – tan65° tan75°. Note that it is only possible to calculate values trigonometric ratios for integral multiples of 1½  degree or 3 deg. so it is possible to calculate tan 75, but not tan 65. Hence the 2^nd part of question is wrong and can not be calculated (except using a calci, which gives an approx value).