If 0 < θ , ϕ < π 2 , x = ∑ n = 0 ∞ cos 2 n θ , y = ∑ n = 0 ∞ sin 2 n ϕ and z = ∑ n = 0 ∞ cos 2 n θ · sin 2 n ϕ then :

Question

If 0 &#60; &#952; , &#981; &#60; &#960; 2 , x = &#8721; n = 0 &#8734; cos 2 n &#952; , y = &#8721; n = 0 &#8734; sin 2 n &#981; and z = &#8721; n = 0 &#8734; cos 2 n &#952; &#183; sin 2 n &#981; then :

Aicharya · Accepted Answer

x = 1 1 - cos 2 &#952; &#8658; sin 2 &#952; = 1 x Also, cos 2 &#952; = 1 y &#160; &#38; &#160; 1 - sin 2 &#952; cos 2 &#952; = 1 z So, 1 - 1 x &#215; 1 y = 1 z &#8658; z x y - 1 = x y ...... i Also, 1 x + 1 y = 1 &#160;&#160; &#8658; x + y = x y ...... ii From i and ii x y + z = x y z = x + y z

If 0 < θ , ϕ < π 2 , x = ∑ n = 0 ∞ cos 2 n θ , y = ∑ n = 0…

Solution

If 0 &#60; &#952; , &#981; &#60; &#960; 2 , x = &#8721; n = 0 &#8734; cos 2 n &#952; , y = &#8721; n = 0…

Solution

If 0 < θ , ϕ < π 2 , x = ∑ n = 0 ∞ cos 2 n θ , y = ∑ n = 0…