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vishweshshrimali5

  • 2 years ago

Solve: \[\large{\theta = \tan^{-1}(2\tan ^2\theta) - \frac{1}{2} \sin^{-1} \frac{3 \sin 2 \theta }{ 5 + 4 \cos 2 \theta }}\]

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  1. vishweshshrimali5
    • 2 years ago
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    @hartnn @amistre64 @Callisto @Hero

  2. amistre64
    • 2 years ago
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    and what is it we are looking to do with this monstrocity?

  3. vishweshshrimali5
    • 2 years ago
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    Solve for theta

  4. vishweshshrimali5
    • 2 years ago
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    (general solutions)

  5. amistre64
    • 2 years ago
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    im just too sick to be able to concentrate on most of that :/

  6. vishweshshrimali5
    • 2 years ago
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    Its OK

  7. vishweshshrimali5
    • 2 years ago
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    Eventhough Thanks for your time

  8. amistre64
    • 2 years ago
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    \[{\theta = \tan^{-1}(2\tan ^2\theta) - \frac{1}{2} \sin^{-1} \frac{3 \sin 2 \theta }{ 5 + 4 \cos 2 \theta }}\] \[{t = \tan^{-1}(2sec^2t-2) - \frac{1}{2} \sin^{-1} \frac{3 \sin 2t }{ 5 + 4 \cos 2t }}\] \[{2t = 2\tan^{-1}(2sec^2t-2) - \sin^{-1} \frac{3 \sin 2t }{ 5 + 4 \cos 2t }}\] yeah, im not going to be able to work it out in this condition :) good luck tho

  9. hartnn
    • 2 years ago
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    maybe use \(arcsin x= 2arctan (x/(1+\sqrt{1-x^2}))\)

  10. harsh314
    • 2 years ago
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    \[\frac{ 1 }{ 2 }\sin^{-1} \frac{ 3\sin \theta }{ 5+4 \cos \theta }\]be assumed as \[ \alpha\] now\[\sin 2\alpha =\frac{ 3 \sin 2 \theta }{ 5+4\cos2 \theta }=m\] suppose now\[m=\frac{ 6 \tan \theta }{ 9+\tan ^{2}\theta } ,\]

  11. harsh314
    • 2 years ago
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    \[\sqrt{\frac{ 1-m }{ 1+m }}=\tan{\frac{ \pi }{ 4 } -\alpha}\] \[\sqrt{\frac{ 1-m }{ 1-m }}=\frac{ 3-\tan \theta }{ 3+\tan \theta }\] \[\frac{ \pi }{ 4 }- \alpha=\tan^{-1} \sqrt{\frac{ 1-m }{ 1+m }}\] substituting these values in the equation we obtain a cubic equation\[\tan ^{3}\theta -3\tan \theta+2=0\] i don't know how to solve it plz kindly tell me still by hit and trial i got pi/4

  12. hartnn
    • 2 years ago
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    to solve, x^3-3x+2=0 i would first note that 1-3+2 =0 hence (x-1) must be the factor, x=1 must be the root tan theta =1 gives theta = pi/4

  13. hartnn
    • 2 years ago
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    to get other 2 roots, we can use synthetic division, taking x=1

  14. harsh314
    • 2 years ago
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    other values are tan theta =2,-1 ,thanks hartnn

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