Question

If x=r SinACosC y=rSinASinC z=rCosA then prove that x2 + y2 =1

Answer 1

Answer:

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

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Answer 2

Answer:

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Step-by-step explanation:

Given, x=rsinAcosC ..equation..1

y=rsinAsinC .....equation 2

z=rcosA .....equation 3

squaring and adding all three equations we get the following

x^2 +y^2+z^2=r^2(sin2Acos2C + sin2Asin2C + cos2A)

=r^2 {sin2A(cos2C + sin2C) + cos2A}

=r^2 {sin2A+ cos2A}

∴x^2 +y^2+z^2=r^2

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