Question

if sintheta + 2costheta = 1 then prove that costheta - 2sintheta = 2

Answer 1

let theta =@ given ,sin@+2cos@=1divide cos@ both side sin@/cos@ +2cos@/cos@=1/cos@tan@+2=sec@ now squaring both side tan^2@+4+4tan@=sec^2@=1+tan^2@
because sec^2x-tan^2x=1
now 4+4tan@=1tan@=-3/4if we assume @ lies between (pi/2, pi)then ,sin@=3/5cos@=-4/5
now LHS=2sin@-cos@put cos and sin value =2 (3/5)-(-4/5)=6/5+4/5=10/5=2=RHS