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Question

If cos1x + cos1y + cos1z = 3π, then the value of xy+yz+zx =

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Solution

As we know that cos1 function is in range (0, π].Hence from the equation, we observe that the only possibility is whencos1x =π, cos1y =π& cos1z =π because the condition is satisfied only when each term attains its maximum.x=y=z=1xy+yz+zx=1+1+1=3.

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