Question #ca93b

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Answer 1 · 2017-03-16T08:40:29

Using formula
$2sin^2theta=1-cos2theta$

we get
$sintheta=sqrt(1/2(1-cos(2xxtheta))$

Putting $theta=75$

$sin75=sqrt(1/2(1-cos(2xx75))$

$=sqrt(1/2(1-cos(180-30))$

$=sqrt(1/2(1+cos30)$

$=sqrt(1/2(1+sqrt3/2)$

$=sqrt(1/8(4+2sqrt3)$

$=sqrt(1/(2*2^2)((sqrt3)^2+2*sqrt3*1+1^2)$

$=1/(2sqrt2)sqrt((sqrt3+1)^2)$

$=1/(2sqrt2)(sqrt3+1)$