Question

Please answer fast important for me

Answer 1

Answer:

x² + y² + z² = r²

Step-by-step explanation:

Given:

x = r sinAcosC

y = r sinAsinC

z = r cosA

LHS:

x² + y² + z²

= (r sinAcosC)² + (r sinAsinC)² + (r cosA)²

= r²[sin²Acos²C + sin²Asin²C + cos²A]

= r²[sin²A(1 - sin²C) + sin²Asin²C + cos²A]

= r²[sin²A - sin²Asin²C + sin²Asin²C + cos²A]

= r²[sin²A + cos²A]

= r²

= RHS

Hope it helps!

Answer 2

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

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

=r2 {sin2A(cos2C + sin2C) + cos2A}

=r2 {sin2A+ cos2A}

∴x2 +y2+z2=r2