Question

if X equal to R sin a into cos b, y equal to R sin a into Sin B, Z equal to R Cos A then X square + Y square + Z square equal to R square​

Answer 1

AnswEr :

• Given ;

⋆ X = R.sinA.cosB —( ! )

⋆ Y = R.sinA.sinB —( !! )

⋆ Z = R.cosA —( !!! )

• To Prove ;

⋆ X² + Y² + Z² = R²

• Proof ;

• Adding (!) , (!!) and (!!!)

» X + Y + Z = R.sinA.cosB + R.sinA.sinB + R.cosA

• Squaring Each Term

» X² + Y² + Z² = R².sin²A.cos²B + R².sin²A.sin²B + R².cos²A

» X² + Y² + Z² = R².sin²A(cos²B + sin²B) + R².cos²A

• (cos²B + sin²B = 1)

» X² + Y² + Z² = R².sin²A × 1 + R².cos²A

» X² + Y² + Z² = R².sin²A + R².cos²A

» X² + Y² + Z² = R²(sin²A + cos²A)

• (sin²A + cos²A = 1)

» X² + Y² + Z² = R² × 1

» X² + Y² + Z² = R² Hence, Proved

Answer 2

soln refers to the attachment