Question

12.If x = r cos a sin ß, y = r cos a cos B and z = r sin a, show that x2 + y2 + z2 = r2​

Answer 1

Answer:

L.H.S=R.H.S

Step-by-step explanation:

Given:

x = r cosa sinb

y = r cosa cosb

z = r sina

To prove x²+y²+z²=r²

LHS given as x²+y²+z²

= r² cos²a sin²b + r² cos²a cos²b + r² sin²a

So, r² cos²a is been taken common

Now,

= r² cos²a(sin²b+cos²b) + r² sin²a

= r² cos²a*1 + r² sin²a [Because sin² a + cos² a =1 ]

= r² cos²a + r² sin²a

= r² sin²a + r² cos²a

= r²(sin²a + cos²a)

= r². 1

= r² (Proved)

Hence, LHS = RHS