GAVITATION-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.

If A=[[-1, -2, -2], [2, 1, -2], [2, -2, 1]] , then adjA=

Prove that : cos^(2)A+cos^(2)(A+pi/3)+cos^(2)(A-pi/3) =1/2[2cos^(2)A+2cos^(2)(A+60^(@))+2cos^(2)(A-60^(@))] =1/2[1+cos2A+1+cos(2A+120^(@))+1+cos(2A-120^(@))] 1/2[3+cos2A+cos(2A+120^(@))+cos(2A-120^(@))] 1/2[3+cos2A+2cos(2A+120^(@)+2A-120^(@))/(2).cos(2A+120^(@)-2A+120^(@))/(2)] =1/2[3+cos2A+2cos2Acos120^(@)] =1/2[3cos2A+2cos2Acos(90^(@)+30^(@))] =1/2[3+cos2A-2.cos2A.(1/2)] =1/2(3+cos2A-cos2A) =3/2 = RHS Hence Proved.

In the species O_(2) , O_(2)^(+) , O_(2)^(-) and O_(2)^(2-) ,the correct decreasing order of bond strength is (A) O_(2) > O_(2)^(+) > O_(2)^(-) > O_(2)^(2-) (B) O_(2)^(+) > O_(2) > O_(2)^(-) > O_(2)^(2-) (C) O_(2)^(2-) > O_(2)^(-) > O_(2)^(+) > O_(2) (D) O_(2)^(-) > O_(2)^(2-) > O_(2) > O_(2)^(+)

2^(2^(2^2))-:((2^2)^2)^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

If A=[[1^(2),2^(2),3^(2)2^(2),3^(2),4^(2)3^(2),4^(2),5^(2)]] then |Adj A|=