(1) Numer WIVISIVI by 5. In AABC, prove that sec(BC) = cosech 2011 marts.

If tan A= 5/2 prove the following 3tan^2A-3sec^2A+4=1

Consider the points A(3,2,4), B(5,8,0) and C(4,5,2).Find the direction ratio of AB and BC. Hence, prove the A, B, C are collinear.

If cot B= 12/5 Prove that tan^2B-sin^2B=sin^4B.sec^2B .

If cot B=(12)/(5), prove that tan^(2)B-sin^(2)B=sin^(4)B sec^(2)B

In an isoceles triangle ABC, AB = AC and angleBAC=90^(@) , the bisector of angleBAC intersects the side BC at the point D. Prove that (sec angleACD)/(sin angleCAD)="cosec"^(2)angleCAD.

The pointsA(0,0), B(10,0),C (5,5sqrt3) are the vertices of the triangle ABC.Find AB,BC,AC and prove that the triangle is equilateral.

Prove that the perimeter of a triangle is greater than the sum of its three medians. Given: AABC in which AD,BE and CF are its medians.To Prove: AB+BC+AC>AD+BE+CF

BL and CM are medians of a triangle ABC right angled at A. Prove that 4 ( BL^2 + CM^2 ) = 5 BC^2 .

In triangleABC, /_C= 90^(@) and P and Q are the midpoints of BC and AC respectively. Prove that AP^(2)+ BQ^(2)= 5PQ^(2) .

If cos A =(21)/(29) and A lies in the fourth quadrant , find "sin" A and tan A . If "sin" A=(21)/(29) and A lies in the second quadrant prove that sec A + tan A=(-5)/(2)