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Consider the equation tan(270° + 0)= 1 - sin∅/cos∅ where 0° <∅ < 360°

(a) Rewrite the equation in terms of sin ∅ only.

(b) Hence solve the equation for 0° < ∅ < 360°.​

Consider the equation tan(270° + 0)= 1 - sin∅/cos∅ where 0° <∅ < 360° (a) Rewrite-example-1
User Baris Erden
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1 Answer

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\\ \sf\longmapsto tan(270+\theta)=1-(sin\theta)/(cos\theta)


\\ \sf\longmapsto (sin(270+\theta))/(cos(270+\theta))=1-(sin\theta)/(cos\theta)


\\ \sf\longmapsto (-cos\theta)/(sin\theta)=1-(sin\theta)/(cos\theta)


\\ \sf\longmapsto(sin\theta)/(cos\theta) (-cos\theta)/(sin\theta)=1


\\ \sf\longmapsto (sin^2\theta-cos^2\theta)/(-cos\theta sin\theta)=1


\\ \sf\longmapsto (-2cos\theta)/(-cos\theta sin\theta)


\\ \sf\longmapsto (2)/(sin\theta)=1


\\ \sf\longmapsto 2cosec\theta=1


\\ \sf\longmapsto cosec\theta=(1)/(2)


\\ \sf\longmapsto \theta=cosec^(-1)\left((1)/(2)\right)

  • theta doesn't exist
User Bob Stein
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