Question

$\sqrt{2} tan \: theta = \sqrt{6} then \: find \: the \: value \: of \: \sin(theta \: + \sqrt{3} cos \: theta$
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Answer 1

Step-by-step explanation:

$\sqrt{2} tan \: x = \sqrt{6} \\ tan \: x = \frac{ \sqrt{6} }{ \sqrt{2} } \\ tan \: x = \sqrt{3} \\ tan \: x = tan \: 60 \\ x = 60$

$sin \: x + \sqrt{3} cos \: x \\ = sin60 + \sqrt{3} cos60 \\ = \frac{ \sqrt{3} }{2} + \frac{ \sqrt{3} }{2} \\ = \sqrt{3}$