((1)/(a)+(1)/(b)-1)/(d theta)=(1)/(a^(3)+b^(3))

int_(0)^((pi)/(2))sinthetacostheta(a^(2)sin^(2)theta+b^(2)cos^(2)theta)^((1)/(2))d theta=(1)/(3)((a^(2)+ab+b^(2))/(a+b))

int_ (0) ^ ((pi) / (2)) sin theta cos theta (a ^ (2) sin ^ (2) theta + b ^ (2) cos ^ (2) theta) ^ ((1) / ( 2)) d theta = ((1) / (3)) ((a ^ (2) + ab + b ^ (2)) / (a + b))

If a:b:c=2:3:4, then (1)/(a):(1)/(b):(1)/(c) is equal to (1)/(4):(1)/(3):(1)/(2) b.4:3:2 c.6:4:3 d.none of these

If cos theta=(1)/(2)(a+(1)/(a)),cos3 theta=lambda(a^(3)+(1)/(a^(3))), then lambda(a)-(1)/(4) (b) (1)/(4) (c) 1 (d) none of these

If (a)/(b)+(b)/(a)=-1, then a^(3)-b^(3)=1(b)-1 (c) (1)/(2)(d)0

If cos theta = 1/2 (a+(1)/(a)), then the value of cos 3 theta is ............. A) 1/8 (a ^(3) +(1)/(a ^(3))) B) 3/2 (a+(1)/(a)) C) 1/2 (a^(3) + (1)/(a^(3))) D) 1/3 (a^(3) +(1)/(a ^(3)))

The value of the determinant Delta = |((1 - a_(1)^(3) b_(1)^(3))/(1 - a_(1) b_(1)),(1 - a_(1)^(3) b_(2)^(3))/(1 - a_(1) b_(2)),(1 - a_(1)^(3) b_(3)^(3))/(1 - a_(1) b_(3))),((1 - a_(2)^(3) b_(1)^(3))/(1 - a_(2) b_(1)),(1 - a_(2)^(3) b_(2)^(3))/(1 - a_(2) b_(2)),(1 - a_(2)^(3) b_(3)^(3))/(1 - a_(2) b_(3))),((1 - a_(3)^(3) b_(1)^(3))/(1 - a_(3) b_(1)),(1 - a_(3)^(3) b_(2)^(3))/(1 - a_(3) b_(2)),(1 - a_(3)^(3) b_(3)^(3))/(1 - a_(3) b_(3)))| , is

If (a)/(b)+(b)/(a)=1, then a^(3)+b^(3)=1(b)-1(c)(1)/(2)(d)0

If |a|<1and|b|<1, then the sum of the series 1+(1+a)b+(1+a+a^(2))b^(2)+(1+a+a^(2)+a^(3))b^(3)+ is (1)/((1-a)(1-b)) b.(1)/((1-a)(1-ab)) c.(1)/((1-b)(1-ab)) d.(1)/((1-a)(1-b)(1-ab))