Question

show that cos42+cos78+cos162=0 give explanation

Answer 1

Cos 42 + cos 78 + cos 162

= cos(60 – 18)+ cos(60+18)+cos(180-18)

now apply formula
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= cos 60 . cos 18 + sin 60 . sin 18 + cos 60 . cos 18 – sin60.sin 18 – cos 18

= 2cos 60 . cos 18 – cos 18

= 2. ½ . cos 18 – cos 18 =0
Hope it's helpful

Answer 2

First, solve cos42 + cos78

As we know
cos A + cos B = 2 cos( A + B/ 2 ) cos( A − B /2 )

so cos42+cos78=2cos60cos18=cos18

Now whats left is cos18+cos162

Use the formula again:

cos18+cos162=2cos(18+162/2)cos(162-18/2)
                       =2cos(90)cos(72)=zero as cos(90)=0

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