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Math Help - Difficult Trigo Problems

  1. #1
    Junior Member
    Joined
    Aug 2009
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    Difficult Trigo Problems

    Hello people,
    Please help me with the following problems. I was unable to solve any of them.

    1) If Cos(a) + Cos(b) + Cos(c) = Sin(a) + Sin(b) + Sin(c) = 0,
    then the value of Cos(3a) + Cos(3b) + Cos(3c) = ?

    2) If [e^cos(x)] - [e^-cos(x)] = 4. Find the value of Cos(x)

    3) If 2Sin^2 \theta = 3 Cos \theta, find the positive angle of \theta

    4) In \triangle ABC, \theta is an acute angle & tan\theta is equal to three times of Cot\theta. Find the value of (sin^2\theta) + (Cosec^2\theta) - (1/2)  (Cot^2\theta)
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  2. #2
    MHF Contributor Amer's Avatar
    Joined
    May 2009
    From
    Jordan
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    1,093
    Quote Originally Posted by saberteeth View Post
    Hello people,
    Please help me with the following problems. I was unable to solve any of them.

    1) If Cos(a) + Cos(b) + Cos(c) = Sin(a) + Sin(b) + Sin(c) = 0,
    then the value of Cos(3a) + Cos(3b) + Cos(3c) = ?

    2) If [e^cos(x)] - [e^-cos(x)] = 4. Find the value of Cos(x)

    3) If 2Sin^2 \theta = 3 Cos \theta, find the positive angle of \theta

    4) In \triangle ABC, \theta is an acute angle & tan\theta is equal to three times of Cot\theta. Find the value of (sin^2\theta) + (Cosec^2\theta) - (1/2)  (Cot^2\theta)

    2) e^{\cos x} - e^{-\cos x} = 4

    e^{2\cos x } - 1 = 4 e^{\cos x}

    e^{2\cos x } - 4e^{\cos x} - 1 =0

    let u=e^{\cos x}

    u^2 - 4u - 1=0

    u=\frac{4 \mp \sqrt{16+4}}{2}

    u=2+\sqrt{5} or  u =2-\sqrt{5}

    e^{\cos x} = 2+\sqrt{5} \Rightarrow  \cos x = \ln (2+\sqrt{5} )

    e^{\cos x } = 2 -\sqrt{5} \Rightarrow \cos x = \ln (2-\sqrt{5})


    3) 2\sin ^2 \theta = 3\cos \theta

    2(1-\cos ^2\theta) = 3\cos \theta

    2\cos ^2\theta +3\cos \theta -2=0

    let u=\cos \theta

    2u^2+3u-2 =0 you can solve it after you find u values find x
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  3. #3
    MHF Contributor Amer's Avatar
    Joined
    May 2009
    From
    Jordan
    Posts
    1,093
    Quote Originally Posted by saberteeth View Post
    Hello people,
    Please help me with the following problems. I was unable to solve any of them.

    1) If Cos(a) + Cos(b) + Cos(c) = Sin(a) + Sin(b) + Sin(c) = 0,
    then the value of Cos(3a) + Cos(3b) + Cos(3c) = ?

    2) If [e^cos(x)] - [e^-cos(x)] = 4. Find the value of Cos(x)

    3) If 2Sin^2 \theta = 3 Cos \theta, find the positive angle of \theta

    4) In \triangle ABC, \theta is an acute angle & tan\theta is equal to three times of Cot\theta. Find the value of (sin^2\theta) + (Cosec^2\theta) - (1/2)  (Cot^2\theta)

    4) \tan \theta = 3 \cos \theta

    \tan \theta = \frac{3}{\tan \theta }

    \tan ^2\theta = 3

    \tan \theta = \sqrt{3} \Rightarrow \theta =\frac{\pi}{3}

    the rest of question just you should know

    \sin \frac{\pi}{3} = ??

    \sec \frac{\pi}{3}= ??

    \cos \frac{\pi}{3} =??
    the rest for you
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