SOLUTION: I am a grade 10 student and we have read abt multiple and sub multiple angles.. I have problem with this questions..I hope that my question will be answered prove that: sin6.s

Question 62060: I am a grade 10 student and we have read abt multiple and sub multiple angles..
I have problem with this questions..I hope that my question will be answered
prove that:
sin6.sin42.sin66.sin78=(1/16)
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
I am a grade 10 student and we have read abt multiple and sub multiple angles..
I have problem with this questions..I hope that my question will be answered
prove that:
sin6.sin42.sin66.sin78=(1/16)
tpt 4sin6*sin48*sin66*sin78=1/4
lhs = (2si6sin66)(2sin42sin78)=[cos60-cos72][cos36-cos120]
=[0.5-cos72][0.5+cos36]
here we have to use the stndard expansions for cos72&cos36
cos72=[sqrt(5)-1]/4.....cos36=[sqrt(5)+1]/4
lhs=0.25+0.5[{sqrt(5)+1}/4-{sqrt(5)-1}/4] - [{sqrt(5)+1}/4][{sqrt(5)-1}/4]
=0.25+0.5*0.5-0.25=0.25=/4=rhs
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