Question

If x = r sinθ cosφ ; y= r sin θ sinφ and z = r cosθ then find​

Answer 1

Answer →

x² +y² +z² = r²

Solution →

let theta = a and fie = b

Here , putting the value of x ,y and z in LHS

→(r sina cosb)² + ( r sina.sinb)² +(r cosa)²

→r²sin²a.cos²b + r² sin²a.sin²b + r²cos²a

Here taking r²sin²a common from 1st 2 terms .

→r²sin²a ( cos²b + sin²b) + r²cos²a

As we know that sin²a + cos²a = 1

→r²sin²a (1) + r²cos²a

→r²sin²a + r²cos²a

Taking r² common

→r²( sin²a + cos²a )

→r²(1)

→r²

So, x²+y²+z² = r² .

hope it helps