Question

a ∆abc is right angled at b ; find the value of sec a .cosec c - tan a .cot c/sin b

Answer 1

if triangle is right angled at b then b= 90°
so acc to question
(sec.a)(cosec.c) - (tan.a)(cot.c)/(sin.b)
if angle a is taken into consideration then
sec.a = ac/ab
tan.a = bc/ab
and
sin.b = sin(90°) = 1
so equation becomes
(ac/ab)(cosec.c) - (bc/ab)(cot.c)
now if angle c is taken into consideration
cosec.c = ac/bc
cot.c = ab/bc
so filling values
(ac × ac)/(ab × bc) - (bc × ab)/(ab × bc)
{ (ac^2) - (ab×bc) }/ (ab)(bcl

Answer 2

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