If x = ∑ n = 0 ∞ - 1 n tan 2 ⁡ θ and y = ∑ n = 0 ∞ cos 2 n ⁡ θ , for 0 < θ < π 4 , then:

Question

If x = &#8721; n = 0 &#8734; - 1 n tan 2 &#8289; &#952; and y = &#8721; n = 0 &#8734; cos 2 n &#8289; &#952; , for 0 &#60; &#952; &#60; &#960; 4 , then:

Aicharya · Accepted Answer

y = 1 + cos 2 &#8289; &#952; + cos 4 &#8289; &#952; + &#8230; Above series is an infinite G.P, apply sum of infinite G.P. &#8658; y = 1 1 - cos 2 &#8289; &#952; &#8658; 1 y = sin 2 &#952; x = 1 1 - - tan 2 &#8289; &#952; = 1 sec 2 &#8289; &#952; &#8658; cos 2 &#8289; &#952; = x &#8658; 1 y + x = 1 &#8658; y 1 - x = 1

If x = ∑ n = 0 ∞ - 1 n tan 2 ⁡ θ and y = ∑ n = 0 ∞ cos 2 n ⁡ θ…

Solution

If x = &#8721; n = 0 &#8734; - 1 n tan 2 &#8289; &#952; and y = &#8721; n = 0 &#8734; cos 2 n &#8289; &#952;…

Solution

If x = ∑ n = 0 ∞ - 1 n tan 2 ⁡ θ and y = ∑ n = 0 ∞ cos 2 n ⁡ θ…