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$prove \: that \: \\ \sin20 \sin40 \sin60 \sin80 = \frac{3}{16}$









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Answer 1

Hello,Buddy!!

||Required Solution||

$\sin(20) . \sin(40) . \sin(60) . \sin(80) \\ \frac{ \sqrt{3} }{2} [ \sin(40) . \sin(20) ] \sin(80) \\ \frac{ \sqrt{3} }{2 \times 2} [2 \sin(40) . \sin(20) ] \sin(80) \\ \frac{ \sqrt{3} }{4} [ \cos(40 - 20) - \cos(40 + 20) ] \sin(80) \\ \frac{ \sqrt{3} }{4} [ \cos(20) - \cos(60) ] \sin(80) \\ \frac{ \sqrt{3} }{4} [ \sin(80) \cos(20) - \frac{1}{2} \sin(80) ] \\ \frac{ \sqrt{3} }{4 \times 2} [2 \sin(80) \cos(20 ) - \sin(80) ] \\ \frac{ \sqrt{3} }{8} [ \sin(80 + 20) + \sin(80 - 20) - \sin(80) ] \\ \frac{ \sqrt{3} }{8} [ \sin(\pi - 100) + \frac{ \sqrt{3} }{2 } - \sin(80) ] \\ \frac{ \sqrt{3} }{8} [ \cancel{\sin(80)} + \frac{ \sqrt{3} }{2} \cancel{- \sin(80)}] \\ \frac{ \sqrt{3} }{8} + \frac{ \sqrt{3} }{2} \\ \frac{3}{16}$

• Hence, Proved.

➪ $\bold{\sin20\sin40\sin60\sin80 = \frac{3}{16}}$

@MrMonarque♡

Hope It Helps You ✌️

Answer 2

Answer:

hello Apidi good evening

kmn acho tumi

Step-by-step explanation:

ami bhalo nei

to kaise he aplog