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Question

If x=a sin A cos C,y=a sin A sin C,z=a cos A shwo that a2=x2+y2+z2 [4 MARKS]

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Solution

Formula: 2 Marks
Proof: 2 Marks

RHS=x2+y2+z2=(a sin A cos C)2+(a sin A sin C)2+(a cos A)2=a2 sin2 A cos2 C+a2 sin2 A sin2 C+a2 cos2 A=a2[sin2 A cos2 C+sin2 A sin2 C+cos2 A]=a2[sin2 A(cos2 C+sin2 C)+cos2 A]=a2(sin2 A+cos2 A)[ cos2 C+sin2 C=1]=a2=LHS

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