Evaluate :
`sqrt( a^(-1 ) b ) sqrt( b^(-1 ) c ) sqrt( c^(-1 ) a ) `

If a,b,c are positive real numbers,then sqrt(a^(-1)b)x sqrt(b^(-1)c)x sqrt(c^(-1)a) is equal to: 1 (b) abc(c)sqrt(abc)(d)(1)/(abc)

Evaluate : ( sqrt( 1 + b ) - 1) / b = a ) b /( sqrt( 1 + b ) - 1) b ) b/( sqrt( 1 + b ) + 1) c ) 1/ ( sqrt( 1 + b ) + 1)

Prove that. (i) sqrt(x^(-1) y) .sqrt(y^(-1) z) . Sqrt(z^(-1) x) = 1 (ii) ((1)/(x^(a-b)))^((1)/(a-c)).((1)/(x^(b-c))).((1)/(x^(c-b)))^((1)/(c-b))= 1 (iii) (x^(a(b-c)))/(x^(b(a-c))) div ((x^(b))/(x^(a))) (iv) ((x^(a+b))^(2)(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))

If cos^(-1)a+cos^(-1)b+cos^(-1)c=pi, then the value of (a sqrt(1-a^(2))+b sqrt(1-b^(2))+c sqrt(1-c^(2))) will be

In a triangle A B C , a line X Y is drawn parallel to B C meeting A B in X and A C in Y . The area of the triangle A X Y is half of the area of the triangle A B C . X Y divides A B in the ratio of 1 :sqrt(2) (b) sqrt(2) :(sqrt(2)-1) (c) 1 :(sqrt(2)-1) (d) sqrt(2) :sqrt(3)

If sin^(-1)a+sin^(-1)b+sin^(-1)c=pi, then a sqrt(1-a^(2))+b sqrt(1-b^(2))+c sqrt(1-c^(2)) is equal to a+b+c( b )a^(2)b^(2)c^(2)2abc(d)4abc

Evaluate : Find the value of sqrt( 3 + sqrt(5)) a ) sqrt(3)/2 + 1/sqrt(2) b ) sqrt(3)/2 - 1/2 c ) sqrt(5)/2 - 1/sqrt(2) d ) sqrt(5)/sqrt(2) + 1/sqrt(2)

Given b=2,c=sqrt(3),/_A=30^(0), then inradius of o+ABC is (sqrt(3)-1)/(2) (b) (sqrt(3)+1)/(2) (c) (sqrt(3)-1)/(4) (d) none of these