Match the following :
Column-IColumn-II(i) If f (x) = cos–1 ( cos x ), f (2009)= aπ + 2009b where a…

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Match the following :
Column-IColumn-II(i) If f (x) = cos–1 ( cos x ), f (2009)= aπ + 2009b where a,b are rational numbers then a/16 + 39b =    [A] 4(ii) a,b∈ and    sin6a + 3sin2a cos2b + cos6 b = 1 then  =[B] 3(iii) In circle of radius 4cm of    a triangle ABC touches the side BC at D. If BD = 6cm DC = 8cm & area    of triangle ABC    is k cm2, then [C] 1(iv) = 8x3 +4x2 –    4x – k    where x    =    cos18°, then value of k is[D] 5

CGP EDU Academic Team · Accepted Answer

The correct answer is CHECK THE SOLUTION.. (i) - [C]
(ii) - [C]
(iii) - [A]
(iv) - [B]
Sol. (i) 639 π < 2009 < 640 π
f (2009) = cos –1 (cos 2009)
= 640 π – 2009
∴ a = 640, b = – 1
(ii) sin 6 a + 3sin 2 a cos 2 b + cos 6 b – 1 = 0
[(sin 2 a + cos 2 b – 1)] [(sin 2 a + 1) 2 + (cos 2 a + 1) 2 + (sin 2 a
– cos 2 b) 2 ] = 0
⇒ sin 2 a + cos 2 b = 1
∴ a = b
⇒ 
(iii)

tan  & tan 
∴ tan  . tan  =  ×

3s – 3a = s
2s = 3a
s = 21 [  a = 14]
Now area of Δ = k = rs = 4 × 21 = 84
∴ 
(iv)  = 4cos 3 18°–3 = 4x 2 –3

= 4cos18°(2cos 2 18°–1) = 8x 3 – 4x
Comparing k = 3

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Similar Questions

Column-I	Column-II
(i) If f (x) = cos–1 ( cos x ), f (2009) = aπ + 2009b where a,b are rational numbers then a/16 + 39b =	[A] 4
(ii) a,b∈ and sin6a + 3sin2a cos2b + cos6 b = 1 then =	[B] 3
(iii) In circle of radius 4cm of a triangle ABC touches the side BC at D. If BD = 6cm DC = 8cm & area of triangle ABC is k cm2, then	[C] 1
(iv) = 8x3 +4x2 – 4x – k where x = cos18°, then value of k is	[D] 5

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