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Question

# Statement 1: If xy+yz+zx=1 where x,y,z∈R+, then x1+x2+y1+y2+z1+z2=2√(1+x2)(1+y2)(1+z2) Statement 2: In a triangle ABC, sin2A+sin2B+sin2C=4sinAsinBsinC

A
Both the statements are TRUE and Statement 2 is the correct explanation of Statement 1
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B
Both the statements are TRUE but Statement 2 is NOT the correct explanation of Statement 1
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C
Statement 1 is TRUE and Statement 2 is FALSE
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D
Statement 1 is FALSE and Statement 2 is TRUE
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Solution

## The correct option is A Both the statements are TRUE and Statement 2 is the correct explanation of Statement 1Let x=cotA,y=cotB,z=cotC ⇒∑cotAcotB=1 ⇒A+B+C=nπ Statement 1: LHS =12[sin2A+sin2B+sin2C] =2sinAsinBsinC RHS =2|cosec A cosec B cosec C| =±2sinAsinBsinC Statement 2 is true as it is a conditional identity.

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