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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 Tan270 0 1 Sincos Where 0 Lt Lt 360 A Rewrite The Equation In Terms Of Sin Only B Hence Solve The Equation For 0 Lt Lt 360 class=

Sagot :

[tex]\\ \sf\longmapsto tan(270+\theta)=1-\dfrac{sin\theta}{cos\theta}[/tex]

[tex]\\ \sf\longmapsto \dfrac{sin(270+\theta)}{cos(270+\theta)}=1-\dfrac{sin\theta}{cos\theta}[/tex]

[tex]\\ \sf\longmapsto \dfrac{-cos\theta}{sin\theta}=1-\dfrac{sin\theta}{cos\theta}[/tex]

[tex]\\ \sf\longmapsto\dfrac{sin\theta}{cos\theta} \dfrac{-cos\theta}{sin\theta}=1[/tex]

[tex]\\ \sf\longmapsto \dfrac{sin^2\theta-cos^2\theta}{-cos\theta sin\theta}=1[/tex]

[tex]\\ \sf\longmapsto \dfrac{-2cos\theta}{-cos\theta sin\theta}[/tex]

[tex]\\ \sf\longmapsto \dfrac{2}{sin\theta}=1[/tex]

[tex]\\ \sf\longmapsto 2cosec\theta=1[/tex]

[tex]\\ \sf\longmapsto cosec\theta=\dfrac{1}{2}[/tex]

[tex]\\ \sf\longmapsto \theta=cosec^{-1}\left(\dfrac{1}{2}\right)[/tex]

  • theta doesn't exist
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