Question

If x cos^3o +y sin^3o =sinocoso and x Coso = ysino then show x^2 + y^2 = 1

Answer 1

Answer:

Therefore x^2+y^2=1

Hence proved

Answer 2

Given:

X*Cos^3O + Y*Sin^3O = SinO*CosO —> 1

X*CosO = Y*SinO —> 2

From Equation 1,

X*CosO*Cos^2O + Y*Sin^3O = SinO*CosO ——> 3

Substitute Equation 2 in equation 3,

Y*SinO*Cos^2O + Y*Sin^3O = SinO*CosO

Y*SinO*(Cos^2O + Sin^2O) = SinO*CosO

Y*SinO*(1) = SinO*CosO

Y = CosO ——> 4

Squaring on both sides,

Y^2 = Cos^2 ——> 5

Substitute equation 4 in equation 2,

X*CosO = CosO*SinO

X = SinO

Squaring on both sides,

X^2 = Sin^2 ——> 6

Adding equations 5 & 6,

X^2 + Y^2 = Sin^2 + Cos^2

X^2 + Y^2 = 1

Hence Proved.