Byrophytes-2

Evaluate : 2/7 times ( -2/2 ) - 2/2 times 2/2 - 2/2 times 2/7

Evaluate : 2/7 times (-2 )/2 - 2/2 times 2/2 - 2/2 times 2/7

Prove that matrix [((b^(2)-a^(2))/(a^(2)+b^(2)),(-2ab)/(a^(2)+b^(2))),((-2ab)/(a^(2)+b^(2)),(a^(2)-b^(2))/(a^(2)+b^(2)))] is orthogonal.

The locus of the foot of perpendicular drawn from the centre of the ellipse x^2+""3y^2=""6 on any tangent to it is (1) (x^2-y^2)^2=""6x^2+""2y^2 (2) (x^2-y^2)^2=""6x^2-2y^2 (3) (x^2+y^2)^2=""6x^2+""2y^2 (4) (x^2+y^2)^2=""6x^2-2y^2

Prove that: cotA/2-tanA/2=(cosA/2)/(sinA/2)-(sinA/2)/(cosA/2) =(cos^(2)A/2-sin^(2)A/2)/(sinA/2cosA/2) =cosA/(1/2.(2sinA/2cosA/2)) =(2cosA)/(sinA)=2cotA = RHS. Hence Proved.

The value of the determinant |{:(1^(2),2^(2),3^(2),4^(2)),(2^(2),3^(2),4^(2),5^(2)),(3^(2),4^(2),5^(2),6^(2)),(4^(2),5^(2),6^(2),7^(2)):}| is

The nth term of the given sequence 3/ (1^ 2) ⋅ 5/ (1^ 2 + 2^ 2) ⋅ 7/ (1^ 2 + 2^ 2 + 3^ 2) ⋅ 9/ (1^ 2 + 2^ 2 + 3^ 2 + 4^ 2)

The sum of the first n terms of the series 1^(2)+2.2^(2)+3^(2)+2.4^(2)+5^(2)+2.6^(2)+... is