How to use t-substitution to solve sinθ - 2cosθ = 2?

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Answer 1 · 2018-05-20T10:45:38

# theta=2arctan2+2kpi, kin ZZ#.

We use, #sintheta=(2t)/(1+t^2), costheta=(1-t^2)/(1+t^2), t=tan(theta/2).#

Sub.ing in the given eqn. we get,

# (2t)/(1+t^2)-2((1-t^2)/(1+t^2))=2#.

#:. 2t-2+2t^2=2+2t^2#.

#:. 2t=4, or, t=2#.

#:. tan(theta/2)=2=tan(arctan2)#.

Since, #tanx=tany rArr x=y+kpi, k in ZZ#, we have,

#theta/2=arctan2+kpi, k in ZZ#.

#:. theta=2arctan2+2kpi, kin ZZ#.