Question

if x=2sina+5cosa and y=2cosa 5sina then prove x2+y2 =29
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Answer 1

Answer:

x=2sinA+5cosA, y=2cosA-5sinA

x²+y²=29

>(2sinA+5cosA)²+(2cosA-5sinA)²=29

>(2sinA)²+2(2sinA)(5-cosA)+(5cosA)²+(2cosA)²-2(2cosA)(5sinA)+(5sinA)²=29

>4sin²A+20sinAcosA+25cos²A+4cos²A-20sinAcosA+25sin²A=29

>4sin²A+4cos²A+25cos²A+25sin²A+20sinAcosA-20sinAcosA=29

>4(sin²A+cos²A)+25(cos²A+sin²A)=29

>4(1)+25(1)=29

>4+25=29

>29=29

LHS=RHS

Hence proved