CBSE Guess > Papers > Question Papers > Class X > 2009 > Mathematics > Mathematics

Q. 19. Find the middle term of the A.P. 10, 7, 4, …, (– 62) .

Sol. 1 ^st term, a = 10
Common difference, d = 7 – 10 = – 3
a_n = – 62
a + (n – 1)d = – 62
10 + (n – 1) (– 3) = – 62
(n – 1) (– 3) = – 62 – 10 = – 72
n – 1 == 24
n = 24 + 1 = 25

Middle term = term term=13^th term

a_n = a + (n – 1)d a₁₃ = a + 12d
a₁₃ = 10 + 12(– 3) = 10 – 36 = – 26

Q. 20. For an acute angle show that

(sin – cosec ) (cos – sec ) =

Sol. LHS = (sin – cosec) (cos – sec )

=

=

=

=

RHS=

=

=…..[ cos2+sin2= 1]

= cos+ sin…(ii)

From (i) and (ii) LHS = RHS

Mathematics 2009 Question Papers Class X
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