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

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