Cos9degrees+ Sin9degrees/Cos9degrees-Sin9degrees= Cot36degrees.

Question

Cos9degrees+ Sin9degrees/Cos9degrees-Sin9degrees= Cot36degrees.

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Evelyn 2 weeks 2021-11-25T07:53:20+00:00 1 Answer 0 views 0

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    2021-11-25T07:55:11+00:00

    Answer:

    LHS = (Cos9° + Sin9°) / (Cos9° – Sin9°)  

    Divide by Nr and Dr  by  Cos9° …

    LHS = (1 + Tan9°) / (1 – Tan9°)

           = (Tan 45° + Tan 9°) / (1 – Tan 45° * Tan 9°)  

           = Tan (45°+9°)  

           = Tan 54°

           = Cot 36°.

    Hope it helps

    And thanks for asking doubt

    To prove : \frac{\cos 9+\sin 9}{\cos 9-\sin 9}=\cot 36

    Proof :

    Take LHS,

    \frac{\cos 9+\sin 9}{\cos 9-\sin 9}

    Take cos 9 common,

    =\frac{1+\frac{\sin 9}{\cos 9}}{1-\frac{\sin 9}{\cos 9}}

    =\frac{1+\tan 9}{1-\tan 9}

    =\frac{\tan 45+\tan 9}{1-\tan 9\tan 45}

    We know formula,

    \tan(A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}

    Here, A=45 and B=9

    =\tan(45+9)

    =\tan(54)

    =\tan(90-36)

    We know, \tan (90-\theta)=\cot \theta

    =\cot 36

    =RHS

    Hence proved.

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