# Maths-1997 -Set III

**15) Evaluate
/3 sec x tan x dx
0 1 + sec2 x**

Ans15)

/3 sec x tan x dx

0 1 + sec2 x

Put sec x = t

sec x tan xdx = dt

Now when x = /3 => t = 2

x = 0 => t = 1

2 dt = tan-1 (t)

1 1 + t2 2

1

tan-1 (2) – tan-1 (1)

= tan-1 (2) – /4

**Q24) Prove that
b+c c+a a+b
q+r r+p p+q
y+z z+x x+y = 2 a b c
p q r
x y z **