Question

Solve Fast !....................

Answer 1

given
tanz+cotz=2
sq. both sides

tan^2z+cot^2z +2=4


tan^2z+cot^2z=2

Q.E.D

Answer 2

tana + cota =2
take square both sides
(tana + cota)² = 2²
tan²a + cot²a +2tana.cota =4

we Know,
tana =1/cota
so,
tan² a + cot²a +2 = 4
tan²a + cot² a = 4 -2 = 2