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Question

The value of the expression $fraction numerator 2 open parentheses sin invisible function application 1 degree plus sin invisible function application 2 degree plus sin invisible function application 3 degree plus horizontal ellipsis plus sin invisible function application 89 degree close parentheses over denominator 2 open parentheses cos invisible function application 1 degree plus cos invisible function application 2 degree plus horizontal ellipsis plus cos invisible function application 44 degree close parentheses plus 1 end fraction$ equals

$\sqrt{2}$
The altitudes are in A.P.
The altitudes are in G.P.
None of these

The correct answer is: $square root of 2$

$rightwards double arrow fraction numerator N to the power of r end exponent over denominator D to the power of r end exponent end fraction equals 2 open curly brackets sin invisible function application 45 degree open square brackets 2 open parentheses cos invisible function application 44 degree plus cos invisible function application 43 degree plus horizontal ellipsis plus cos invisible function application 1 degree close parentheses close square brackets plus 1 close curly brackets$
$equals 2 sin invisible function application 45 degree$
$equals square root of 2$

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