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If x=cos55,y=cos65,z=cos175 then what is the value of xy+yz+zx?

sanvy , 7 Years ago
Grade 12
anser 1 Answers
Harshit

Last Activity: 7 Years ago

= cos55cos65+cos175cos65+cos175cos55
= cos65(cos55+cos175)+cos175cos55
= cos65(2cos115cos65)+cos175cos55   [cosA+cosB=12cos( A+B/2 )cos( A-B/2 )]
= cos65cos115+cos(180-5)cos55           [cos175=cos(180-5)=-cos5, cos60= ½ ]
=cos65cos115-cos5cos55
= ½ [2cos65cos115-2cos5cos55]
= ½ [cos180+cos50-(cos60+cos50)]      [2cosAcosB=cos(A+B)cos(A-B)]
= ½ [cos180-cos60]
= ½ [0-½]
= – ¼

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