# If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ – y cos θ = 0, then prove that x2 + y2 = 1, (where, sin θ ≠ 0 and cos θ ≠ 0).

Please show work

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Please show work

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**Solutions **

**Let the breadth of the rectangular park br represented by = x metres**

**Therefore, length of the rectangular park be represented by = (x+ 40) meters.**

So, area of the rectangular park = (x + 40) ∙ x square meters

According to the problem we get,

(x + 40) ∙ x = 2304

or, x^2 + 40x = 2304

or, x2 + 40x - 2304 = 0 .................... (i)

or we can do

Let the length of the rectangular park = x metres

Therefore, the breadth of the rectangular park =(x - 40) metres

Area of the rectangular park = x(x - 40) square metres

According to the problem we get,

x(x - 40) = 2304

or,x2 - 40x - 2304 = 0 .................... (ii)

**Both of (i) and (ii) are quadratic equations.**