Question #72b1b

1 Answer
Feb 18, 2018

No Solutions(Ø)

Explanation:

#(1-tanx)^2=sec^2x-2secx#
#2secx-sec^2x+(1-tanx)^2=0#

We know that #tan^2x+1=sec^2x#,
Therefore,
#2secx-2tanx=0#
#secx-tanx=0#
#1/cosx-sinx/cosx=0#
#1/cosx(1-sinx)=0#
#therefore 1/cosx=0 or 1-sinx=0#

#-sinx=-1#(Assuming that #cosx≠0#)
#sinx=1#, #therefore x=2npi+pi/2(But cosx≠0)#
The roots #2npi+pi/2# doesn't satisfies #cosx≠0# for all #n∈ZZ#

Therefore #therefore#No Solutions#(x∈Ø)#