Question

if x=r cos A sin B ,y = r cos A cosB and z=r sinA ,then prove that X2+y2+z2=r2 ​

Answer 1

Step-by-step explanation:

according to question,

x2+y2+z2=

(r cos A sinB)2+(rcosA cosB)2+(rsinA)2

r2cos2A sin2B+r2cos2A cos2B+r2sin2A

r2cos2A (sin2B+cos2B)+r2sin2A.

r2cos2A+r2sin2A.

r2(cos2A+sin2 A)

=r2 proved