If x=aCosθCosΦ, y = aCosθSinΦ and z= aSinθ, then the value of $$x^2+ y^2 + z^2$$ is

Expression 1 : $$x=acos\theta cos\phi$$

Squaring both sides, => $$x^2=a^2cos^2\theta cos^2\phi$$ -------------(i)

Expression 1 : $$y=acos\theta sin\phi$$

Squaring both sides, => $$y^2=a^2cos^2\theta sin^2\phi$$ -------------(ii)

Expression 1 : $$z=asin\theta$$

Squaring both sides, => $$z^2=a^2sin^2\theta$$ -------------(iii)

Adding equations (i),(ii) and (iii)

=> $$x^2+y^2+z^2=(a^2cos^2\theta cos^2\phi)+(a^2cos^2\theta sin^2 \phi)+(a^2sin^2\theta)$$

=> $$x^2+y^2+z^2=a^2cos^2\theta (cos^2\phi+sin^2\phi)+a^2sin^2\theta$$

=> $$x^2+y^2+z^2=a^2cos^2\theta+a^2sin^2\theta$$

=> $$x^2+y^2+z^2=a^2(cos^2\theta+sin^2\theta)$$

=> $$x^2+y^2+z^2=a^2$$

=> Ans - (D)