If tanx/(1-cotx) + cotx/(1-tanx) = -1, what is the value of tanx?

Question

#tanx/(1-cotx) + cotx/(1-tanx) = -1#

395 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-16T00:08:20

#tanx/(1-cotx) + cotx/(1-tanx) = -1#

#=>-tanx/(1-1/tanx) - (1/tanx)/(1-tanx) = 1#

#=>-tan^2x/(tanx-1) - 1/(tanx(1-tanx) )= 1#

#=>tan^2x/(1-tanx) - 1/(tanx(1-tanx) )= 1#

#=>(tan^3x - 1)/(tanx(1-tanx) )= 1#

#=>((tanx - 1)(tan^2x+tanx+1))/(tanx(1-tanx) )= 1#

#tanx=1# will make LHS undefined so neglected.
Hence

#=> - (tan^2x+tanx+1)/tanx= 1#

#=> tan^2x+2tanx+1= 0#

#=>( tanx+1)^2= 0#

#=>tanx=-1#