Question

if [a-b]=135 show that [1-tan a][1+tan b]=2

Answer 1

Answer:

a-b=135

a=135+b

LHS=(1-tana)×(1+tanb)

=(1-tan(135+b))×(1+tanb)

=(1-tan(90+45+b))×(1+tanb)

=(1-tan(90+(45+b)))×(1+tanb)

=(1+cot(45+b))×(1+tanb)

=(1+1/tan(45+b))×(1+tanb)

=(1+(1-tan45.tanb)/(tan45+tanb))×(1+tanb)

now put tan45=1 and do simplification you will be left with 1+1=2

tan45+tanb))×(1+tanb)