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Recent questions tagged p157

If $\cos \alpha +\cos \beta + \cos \gamma = 0 = \sin \alpha + \sin \beta + \sin \gamma$, prove that $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = 0$

asked Jun 11, 2013 by sreemathi.v

1 answer

If $\cos \alpha +\cos \beta + \cos \gamma = 0 = \sin \alpha + \sin \beta + \sin \gamma$, prove that $\sin 3\alpha + \sin 3\beta + \sin 3\gamma = 3 \sin\left ( \alpha +\beta + \gamma \right )$

asked Jun 11, 2013 by sreemathi.v

1 answer

Prove that $\left ( 1+\mathit{i} \right )^{4n}$ and $\left ( 1+\mathit{i} \right )^{4n+2}$ are real and purely imaginary respectively.

asked Apr 16, 2013 by geethradh

1 answer

Prove that $\left ( 1+ \cos \; \theta + \mathit{i}\sin \; \theta \right )^{\mathit{n}} + \left ( 1+ \cos \; \theta - \mathit{i}sin \; \theta \right )^{\mathit{n}} = 2^{\mathit{n+1}} \cos ^{\mathit{n}}\left ( \large\frac{\theta}{2} \right )$$ \cos \;\large\frac{n\theta }{2}$

asked Apr 16, 2013 by geethradh

1 answer

Prove that $\left ( 1+ \mathit{i\sqrt{3}} \right )^{\mathit{n}} + \left ( 1- \mathit{i\sqrt{3}} \right )^{\mathit{n}} = 2^{n+1} \cos \; \large\frac{n\pi}{3}$

asked Apr 16, 2013 by geethradh

1 answer

Prove that $\left ( 1+\mathit{i} \right )^{\mathit{n}} + \left ( 1-\mathit{i} \right )^{\mathit{n}} = 2^{\large\frac{n+2}{2}} \cos \; \large\frac{n\pi}{4}$

asked Apr 16, 2013 by geethradh

1 answer

If $ \cos\;\alpha + \cos\;\beta + \cos\;\gamma = 0 = \sin \;\alpha + \sin \;\beta + \sin \;\gamma $, prove that $\cos^{2}\;\alpha + \cos^{2}\;\beta + \cos^{2}\;\gamma = \sin^{2} \alpha + \sin^{2}\beta + \sin^{2}\gamma = \large\frac{3}{2}$.

asked Apr 10, 2013 by geethradh

1 answer

If $ \cos\;\alpha + \cos\;\beta + \cos\;\gamma = 0 = \sin \;\alpha + \sin \;\beta + \sin \;\gamma $, prove that $\sin 2\alpha + \sin 2\beta + \sin 2\gamma = 0$

asked Apr 8, 2013 by geethradh

1 answer

If $ cos\;\alpha + cos\;\beta + cos\;\gamma = 0 = sin\;\alpha + sin\;\beta + sin\;\gamma $, prove that $ cos\;2\alpha + cos 2\;\beta + cos\;2\gamma = 0$

asked Apr 5, 2013 by geethradh

0 answers

If $ cos \;\alpha + cos \;\beta + cos \;\gamma = 0 = sin \;\alpha + sin \;\beta + sin \; \gamma $, prove that $ sin \;3\alpha \; + \;sin \;3\beta + sin \;3\gamma = 3 sin\left ( \alpha\; + \;\beta\; + \;\gamma \;\right )\Large$

asked Apr 5, 2013 by geethradh

0 answers

If $\cos \alpha + cos \beta + cos \gamma = 0 = sin \alpha + sin \beta + sin \gamma$, prove that $cos 3\alpha + cos 3\beta + cos 3\gamma = 3 cos\left ( \alpha +\beta + \gamma \right )$

asked Apr 4, 2013 by geethradh

1 answer

Simplify: $\Large\frac{\left (cos \;\alpha + \mathit{i} sin \; \alpha \right )^{3}}{\left (sin \;\beta + \mathit{i} cos \;\beta \right)^{4} } \Large$

asked Apr 4, 2013 by geethradh

1 answer

Simplify: $\Large\frac{\left ( cos2 \theta -\mathit{i}sin2 \theta \right )^{7} \left ( cos 3 \theta +\mathit{i} sin3 \theta \right )^{-5}}{\left (cos 4 \theta + \mathit{i} sin4 \theta \right )^{12} \left ( cos 5 \theta -\mathit{i}sin5 \theta \right )^{-6}}\Large$

asked Apr 4, 2013 by geethradh

1 answer

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