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
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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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