Question

State whether the following statement is true or false.

If $cos\alpha +cos\beta +cos\gamma =sin\alpha +sin\beta +sin\gamma =0$, then :
$cos2\alpha +cos2\beta +cos2\gamma =sin2\alpha +sin2\beta +sin2\gamma =0$

• A. True
• B. False

Answer 1

The correct option is A True

Let $Z=e^{i(\alpha +\beta +\gamma )}=0$

Therefore, $cos\alpha +cos\beta +cos\gamma =0$ & $sin\alpha +sin\beta +sin\gamma =0$

Now,

$Z^2=0(Z=0)$

therefore, $e^{2i(\alpha +\beta +\gamma )}=0$

or $e^{i(2\alpha +2\beta +2\gamma )}=0$

therefore, $cos2\alpha +cos2\beta +cos2\gamma =sin2\alpha +sin2\beta +sin2\gamma =0$

Hence the above statement is true.