Question

If x=rsinAcosC y=rsinAsinC and z=rcosA prove that r^2 = x^2 +y^2+z^2

Answer 1

$\huge\bf\mathfrak{SOLUTION}$

Given, x=rsinAcosC ..equation..1

y=rsinAsinC .....equation 2

z=rcosA .....equation 3

squaring and adding all three equations we get the following

x2 +y2+z2=r2(sin2Acos2C + sin2Asin2C + cos2A)

=r2 {sin2A(cos2C + sin2C) + cos2A}

=r2 {sin2A+ cos2A}

∴x2 +y2+z2=r2

Answer 2

hope it would be help ful

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