The value of sin 2-18-sin 2-9-sin 27 -18-sin 24 -9 is

The correct option is B 2 We have, sin^2 (π/18 )+ sin^2 (π/9 ) + sin^2 (7 π/18 ) + sin^2 (4 π/9 ) = 1/2 [ 1 cos (π/9 )+1 cos (2 π/9 )+1 cos 7 π/9 + 1 cos 8 ...

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Standard XII

Mathematics

Trigonometric Ratios of Multiples of an Angle

The value of ...

Question

The value of $s i n^{2} (\frac{π}{18}) + s i n^{2} (\frac{π}{9}) + s i n^{2} (\frac{7 π}{18}) + s i n^{2} (\frac{4 π}{9})$ is

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none of these

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Solution

The correct option is B
2

We have,

$s i n^{2} (\frac{π}{18}) + s i n^{2} (\frac{π}{9}) + s i n^{2} (\frac{7 π}{18}) + s i n^{2} (\frac{4 π}{9}) = \frac{1}{2} [1 - c o s (\frac{π}{9}) + 1 - c o s (\frac{2 π}{9}) + 1 - c o s \frac{7 π}{9} + 1 - c o s \frac{8 π}{9}] (∵ s i n^{2} θ = \frac{1 - c o s 2 θ}{2}) = \frac{1}{2} [4 - c o s (\frac{π}{9}) - c o s (\frac{2 π}{9}) - {- c o s (π - \frac{7 π}{9})} - {- c o s (π - \frac{8 π}{9})}] = \frac{1}{2} [4 - c o s (\frac{π}{9}) - c o s (\frac{2 π}{9}) + (\frac{2 π}{9}) + c o s (\frac{π}{9})] = \frac{4}{2} = 2$

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Similar questions

$s i n^{2} \frac{π}{18} + s i n^{2} \frac{π}{9} + s i n^{2} \frac{7 π}{18} + s i n^{2} 4 \frac{π}{9} =$

{sin}^{2} \frac{π}{18} + {sin}^{2} \frac{π}{9} + {sin}^{2} \frac{7 π}{18} + {sin}^{2} \frac{4 π}{9} = k

. Find the value of

k

Prove that: $s i n^{2} \frac{π}{18} + s i n^{2} \frac{π}{9} + s i n^{2} \frac{7 π}{18} + s i n^{2} \frac{4 π}{9} = 2$

Q. sin²π/18 + sin²π/9 + sin² 7π/18 + sin² 4π/9 =
(a) 1
(b) 4
(c) 2
(d) 0

{sin}^{2} \frac{π}{18} + {sin}^{2} \frac{2 π}{18} + {sin}^{2} \frac{4 π}{18} + {cos}^{2} \frac{π}{18} + {cos}^{2} \frac{2 π}{18} + {cos}^{2} \frac{4 π}{18}

is equal to

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The value of sin2 (π18)+sin2(π9)+sin2 (7π18)+sin2 (4π9) is

The correct option is B 2 We have, sin2 (π18)+ sin2 (π9)+sin2(7π18)+sin2 (4π9)=12[1−cos(π9)+1−cos(2π9)+1−cos7π9+1−cos8π9] (∵ sin2 θ=1−cos 2θ2)=12 [4−cos(π9)−cos(2π9)−{−cos(π−7π9)}−{−cos(π−8π9)}]=12 [4−cos(π9)−cos(2π9)+(2π9)+cos(π9)]=42=2

The value of $s i n^{2} (\frac{π}{18}) + s i n^{2} (\frac{π}{9}) + s i n^{2} (\frac{7 π}{18}) + s i n^{2} (\frac{4 π}{9})$ is