Find the exact value? 2sinxcosx+sinx-2cosx=1

1 Answer
May 9, 2018

rarrx=2npi+-(2pi)/3 OR x=npi+(-1)^n(pi/2) where nrarrZ

Explanation:

rarr2sinx*cosx+sinx-2cosx=1

rarrsinx(2cosx+1)-2cosx-1=

rarrsinx(2cosx+1)-1(2cosx+1)=0

rarr(2cosx+1)(sinx-1)=0

Either, 2cosx+1=0

rarrcosx=-1/2=-cos(pi/3)=cos(pi-(2pi)/3)=cos((2pi)/3)

rarrx=2npi+-(2pi)/3 where nrarrZ

OR, sinx-1=0

rarrsinx=1=sin(pi/2)

rarrx=npi+(-1)^n(pi/2) where nrarrZ