10 let Q.15 25+1 (A) 2 > If a = sin...
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10 let Q.15 25+1 (A) 2 > If a = sin 47° + sin 61° – sin 11° - sin 250 then 3+1 (B) a < 212 (C) 2 > cos 1 (D) 2
JEE/Engineering Exams
Maths
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[ begin{array}{l} sin 47^{circ}+sin 61^{circ}-sin 11^{circ}-sin 25^{circ} left(sin 47^{circ}-sin 25^{circ}right)+left(sin 61^{circ}-sin 11^{circ}right) end{array} ] We Know, [ sin A-sin B=2 cos left(frac{A+B}{2}right) sin left(frac{A-B}{2}right) ] ( therefore quad 2 cos 36^{circ} sin 11^{circ}+2 cos 36^{circ} sin 25^{circ} ) ( Rightarrow 2 cos 36^{circ}left(sin 11+sin 25^{circ}right) ) ( Rightarrow sin A+sin B=2 sin left(frac{A+B}{2}right) cos left(frac{A-B}{2}right) ) ( Rightarrow 2 cos 36^{circ}left(2 sin 18^{circ} cos 7^{circ}right) ) ( Rightarrow 4 cos 36^{circ} sin 18^{circ} cos 7^{circ} ) ( Rightarrow quad 4left(frac{sqrt{5}+1}{4}right)left(frac{sqrt{5}-1}{4}right)^{0}=7^{circ} ) ( Rightarrow quad frac{(sqrt{5})^{2}-1}{4} cos 7^{circ}=cos 7^{circ} )

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