Question

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

Answer 1

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.