Q.12 The value of sin 78° - sin 66°...
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Q.12 The value of sin 78° - sin 66° - sin42° + sin 6° (B) - (D) None of these (C) -1

JEE/Engineering Exams
Maths
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( begin{aligned} & sin 78-sin 66-sin 42+sin 6 =&(sin 78-sin 42)-(sin 66-sin 6) =&[sin (60+18)-sin (60-18)]-[2 cos 36 cdot sin 30] =&[sin 60 cdot cos 18+cos 60 cdot sin 18-sin 60 cdot cos 18+cos 60 cdot sin 18]-2 times cos (90-54) times frac{1}{2} =& 2 cos 60 cdot sin 18 =& 2 times frac{1}{2} times sin 18-sin 54 =& sin 18-sin 54 =& frac{sqrt{5}-1}{4}-frac{sqrt{5}+1}{4} =& frac{sqrt{5}-1-sqrt{5}-1}{4} =&-frac{2}{4} =&-frac{1}{2} end{aligned} )
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