Question

integration :e to the power ax into sinh

Answer 1

Sol:
Triangle ABC is right angled at C.Let BC = a, CA = b, AB = c.


(i) Area of ΔABC = 1/2 × Base × Height = 1/2 × BC × AC = 1/2 ab
Area of ΔABC = 1/2 × Base × Height = 1/2 × AB × CD = 1/2 cp
⇒ 1/2 ab = 1/2 cp
⇒ ab = cp
Hence proved.

(ii) In right angled triangle ABC,
AB2 = BC2 + AC2
c2 = a2 + b2
(ab/p)2 = a2 + b2
a2b2/p2 = a2 + b2 -------- From proof (1)
1/p2 = (a2 + b2) / a2b2
1/p2 = (a2 / a2b2 + b2/ a2b2)
1/p2 = (1/b2 + 1/a2)
1/p2 = (1/a2 + 1/b2)

Hence proved.