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sarah110128

prove: (1+cosθ+cos2θ)/(sinθ+sin2θ)=cotθ

  • one year ago
  • one year ago

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  1. ajprincess
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    \(\cos2\theta=2\cos^2\theta-1\) \(\sin2\theta=2\sin\theta\cos\theta\) using these see if u can do. If u find any difficulties and need some more help plz ask:)

    • one year ago
  2. AnimalAin
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    \[ (1+\cosθ+\cos2θ)/(\sinθ+\sin2θ)=\cotθ \implies\]\[ \cosθ+2\cos^2θ =\frac{\cos \theta}{\sin \theta}(\sin \theta+2 \sin \theta \cos \theta)=\cos \theta + 2 \cos^2 \theta\]

    • one year ago
  3. sarah110128
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    prove: (1+cosθ+cos2θ)/(sinθ+sin2θ)=cotθ (1+cosθ+cos2θ)/(sinθ+2sinθcosθ) (cosθ+cos θ⁡ )/(sinθ+sinθ) cos2θ/sin2θ (2〖cos〗^2 θ-1)/2cosθsinθ (cosθ-1)/sinθ not sure where i went wrong... :/

    • one year ago
  4. ajprincess
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    Taking the expression in the left hand side \[\frac{1+\cos\theta+\cos2\theta}{\sin\theta+\sin2\theta}\] \[=\frac{1+\cos\theta+2\cos^2\theta-1}{\sin\theta+2\sin\theta\cos\theta}\] factor out \(\cos\theta\) from numerator and \(\sin\theta\) from denominator \[=\frac{\cos\theta+2\cos^2\theta}{\sin\theta+2\sin\theta\cos\theta}\] \[=\frac{\cos\theta(1+2\cos\theta)}{\sin\theta(1+2\cos\theta)}\] cancelling the common factor \((1+2\cos\theta)\) \[=\frac{\cos\theta}{\sin\theta}\] \[=\cot\theta\] nw we have shown that lhs=rhs hence proved

    • one year ago
  5. ajprincess
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    Is that clear @sarah11028

    • one year ago
  6. sarah110128
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    Sometimes I wonder why I'm even doing maths....hahaha thank you for you help! :)

    • one year ago
  7. ajprincess
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    welcome:) it is really easy if practice a bit:)

    • one year ago
  8. sarah110128
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    haahha lets hope it get easy! :) And hopefully it'll be my last year of maths

    • one year ago
  9. sarah110128
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    Cos3θ=4cos^3θ-3cosθ (I am trying to prove this identity) cos3θ = cos(θ+2θ) = cosθ cos2θ - sinθ sin2θ = cosθ (2cos^2θ - 1) - 2sin^2θ cosθ (basically here can you please explain how to go from sinθ sin2θ ->2sin^2θ cosθ ) = 2cos^3θ - cosθ - 2(1-cos^2θ) cosθ = 4cos^3θ - 3cosθ thanks

    • one year ago
  10. sarah110128
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    @ajprincess

    • one year ago
  11. ajprincess
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    \[\sin2\theta=2\sin\theta\cos\theta\] \[\sin2\theta*\sin\theta=2\sin\theta\cos\theta*\sin\theta\] \[=2\sin\theta*\sin\theta*cos\theta\] \[=2\sin^2\theta\cos\theta\] Is that clear?

    • one year ago
  12. ajprincess
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    \[\sin2\theta=\sin(\theta+\theta)\] \[=\sin\theta\cos\theta+\cos\theta\sin\theta\] \[=2\sin\theta\cos\theta\]

    • one year ago
  13. ajprincess
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    getting it @sarah110128?

    • one year ago
  14. sarah110128
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    ohh thanks, you've been a great help! :)

    • one year ago
  15. ajprincess
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    welcome:)

    • one year ago
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