sin150°/sin15° = sin30°/sin15°
= 2sin15°cos15°/sin15°
= 2cos15°
= 2cos(45°-30°)
= 2(cos45°cos30°+sin30°sin30°)
= 2(√2/2*√3/2+√2/2*1/2)
= (√6+√2)/2
sin150°=sin30° =1/2
sin15°
=√[ (1- cos30°)/2 ]
=√[ (1- √3/2)/2 ]
=√[(2- √3)/4 ]
=(1/2) √(2- √3)
=(1/2) [√2( √3 -1) /2 ]
= √2( √3 -1) /4
sin150°/sin15°
=(1/2) /[√2( √3 -1) /4]
= 2/[√2( √3 -1) ]
=√2/(√3 -1)
=√2(√3 +1) /2
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