if tanx-tan2x =1,then the value of tan4x-2tan3x-tan2x +2tanx+k=4,then k is equal to - Maths - Trigonometric Functions

Question

if tanx-tan2x =1,then the value of
tan4x-2tan3x-tan2x +2tanx+k=4,then
k is equal to

Neha Sethi · Accepted Answer

tan4x-tan2x-2tan3x+2tanx=4-k⇒tan2xtan2x-1-2tanxtan2x-1=4-k⇒tan2x-2tanxtan2x-1=4-k⇒tanx-1-2tanxtanx-1-1=4-k    as  tanx-tan2x=1⇒tan2x=tanx-1⇒-1+tanxtanx-2=4-k⇒tanx-2+tan2x-2tanx=k-4⇒tan2x-tanx=k-2       as  tanx-tan2x=1⇒-1=k-2⇒k=1