Prove that:`|(4,-8),(7,2)|=8|(5,4),(3,4)|`

Write D_x for the following simultaneous equations 3x+4y=8,x-2y=5 a) |(3,4),(1,-2)| b) |(8,4),(5,-2)| c) |(4,8),(-2,5)| d) |(3,8),(1,5)|

Verify that (3,4,5),(5,12,13),(8,15,17),(24,25,7) are the Pythagorean triplets

Prove that : 2 tan^(-1)""(1)/(5)+sec^(-1)""(5sqrt(2))/(7)+2tan^(-1)""(1)/(8)=(pi)/(4)

Show that A(-4,-7), B(-1,2), C(8,5) and D(5,-4) are the vertices of a parallelogram.

Prove that: sin^(2) (pi/8) +sin^(2) ((3pi)/8) +sin^(2)((5pi)/8)+sin^(2)((7pi)/8)=2

Without expanding,find the values of the following determinants: |(8,2,7),(12,3,5),(16,4,3)|

Show that square ABCD is a parallelogram if A (4,8) ,B(5,5), C(2,4) ,D(1,7) .

A(-4,-7),B(-1,2),C(8,5) and D(5,-4) are the vertices of rhombus ABCD.