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\cos 52^{0}+\cos 68^{0}+\cos 172^{0}

Answer»

First of all cos 172 = -cos 8So now we have= cos 52 + cos 68 - cos 8

Applying Identity,cos A − cos B = −2 sin ½ (A + B) sin ½ (A − B)

let's look at our cos 52 - cos8, here let's A = 52, B=8cos 52 - cos 8 = -2sin[60/2]sin[44/2]cos52 -cos8 = - sin 22socos 52 + cos 68 + cos172= cos52 + cos68 - cos8= cos52 - cos8 + cos68= - sin22 + cos68but by the complementary relationshipsin 22 = cos68 , (since 22+68 = 90)so finally= -cos 68 + cos 68= 0



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