Question

If x= r sin alpha cos beta , y= r sin alpha sin beta and z=r cos alpha , then

Answer 1

Answer:

X^2+y^2+z^2=

R^2Cos^2alphasin^2beta + r^2cos^2alphacos^2beta+ R^2sin^2 alpha

R^2[Cos^2alpha(sin^2beta+ cos^2 beta)+sin^2 alpha]

R^2[Cos^2 alpha + sin^2 alpha]=r^2

Answer 2

Answer:

Solution

We have, x

2

+y

2

+z

2

=r

2

sin

2

αcos

2

β+r

2

sin

2

αsin

2

β+r

2

cos

2

α

=r

2

sin

2

α(cos

2

β+sin

2

β)+r

2

cos

2

α

=r

2

sin

2

α+r

2

cos

2

α

=r

2

Hence, proved.

Step-by-step explanation:

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