Math, asked by Kaaviya1808, 7 months ago

if x=c cos a sin b ; y=c cos a cos b and z= c sin a, show that x^2+y^2+z^2=c^2

Answers

Answered by ritikahirve
1

Step-by-step explanation:

We have,

x=asecθcosϕ

ax=secθcosϕ

 

On squaring both sides, we get

a2x2=sec2θcos2ϕ                      ……. (1)

 

Now, y=bsecθsinϕ

by=secθsinϕ

 

On squaring both sides, we get

b2y2=sec2θsin2ϕ                      ……. (2)

 

Now, z=ctanθ

cz=tanθ

 

On squaring both sides, we get

c2z2=tan2θ                      ……. (3)

 

On adding equation (1) and (2), we have,

a2x2+b2y2=sec2θcos2ϕ+sec2θsin2ϕ

a

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