Question #73c4a

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Answer 1 · 2017-08-11T17:04:26

$4x.$

We will frequently use the Identity : $sin2A=2sinAcosA.$

Also, we need, $costheta=sin(90-theta).$

We have,

$sin24/sin8+cos24/cos8=(sin24cos8+cos24sin8)/(sin8cos8),$

$={sin(24+8)}/(sin8cos8),$

$=sin32/(sin8cos8)=(2sin32)/(2sin8cos8),$

$=(2sin32)/sin16,$

$={2(2sin16cos16)}/sin16,$

$=4cos16=4sin(90-16)=4sin74.$

$rArr sin24/sin8+cos24/cos8=4x.$