anonymous
  • anonymous
given that sin theta+2 cos theta=1,then prove that 2 sin theta-cos theta=2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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AkashdeepDeb
  • AkashdeepDeb
\[\sin \theta+2 \cos \theta=1 \] \[\sin \theta=1-2 \cos \theta\] Square both sides and use identity \[\sin^2 \theta = 1 + 4\cos^2 \theta - 4\cos \theta\] \[1 - \cos^2 \theta =1+4\cos^2θ−4\cosθ\] \[4\cos \theta = 5 \cos^2 \theta\] \[\cos \theta = 4/5\] Now try to calculate!
AkashdeepDeb
  • AkashdeepDeb
Do not do the last 2 steps like that. Take cos theta as x and then find out the solution of the quadratic equation 5x^2 - 4x = 0 Understood? :)

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