Find all solutions to the equation tant 1tan t in the inter

Find all solutions to the equation tan(t) = 1/tan (t) in the interval 0 lessthanorequalto t lessthanorequalto 2 pi. First estimate the solutions from a graph, then find exact answers (given as fractions, not decimals). Enter your answers as a comma separated list.

Solution

tan t= 1/tan t

tan²t=1

tan t=+-1

tan t=1 and tan t=-1

t=pi/4,5pi/4 and t= 3pi/4,7pi/4

t=pi/4,3pi/4, 5pi/4,7pi/4