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Find value of Cos20+cos40+cos60-4cos10cos20cos30.find value

Find value of Cos20+cos40+cos60-4cos10cos20cos30.find value

Grade:11

1 Answers

Rae
25 Points
3 years ago
cos20+ cos40+ cos60 – [4cos10cos20cos30 ](2sin10)/(2sin10)
 
cos20+ cos40 can be written as 2cos30cos10.....by sum to product rule.
 
We get,
           2cos30cos10 + cos60 –[ 4(2sin10cos10)cos20cos30]/2sin10
 
           2(√3/2)cos10 + (1/2) – [4(sin20)cos20cos30]/2sin10
 
           √3cos10 +1/2 – [2(2sin20cos20)cos30]/2sin10
Taking LCM,
 
        [  √3∙2sin10cos10+ sin10 – 2(sin40)cos30 ]/2sin10
        [  √3sin20 + sin10 – 2sin40(√3/2) ]/2sin10
        [  √3sin20 – √3sin40 +sin10 ]/2sin10
        [  √3(sin20 – sin40) +sin10 ]/2sin10
        [  √3( 2sin10cos30 + sin10 ]/2sin10
        [   √3(√3sin10 + sin10) ]/2sin10
        √3sin10(√3 +1)/2sin10
 
        ANS- √3(√3+1)/2
       
                                    

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