Sin 2-18-sin 2-9-sin 27 -18-sin 2 4 -9-

The correct option is C 2 2 We hav: sin^2 π/18+sin^2 π/9+sin^2 7 π/18+sin^2 4 π/9 =sin^2 π/18+sin^2 2 π/18+sin^2 7 π/18+sin^2 8 π/18 =sin^2 π/18+sin^2 2 π/18+s ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Allied Angles

sin 2π/18+sin...

Question

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

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Solution

The correct option is C
2

2

We hav:

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

$= s i n^{2} \frac{π}{18} + s i n^{2} \frac{2 π}{18} + s i n^{2} \frac{7 π}{18} + s i n^{2} \frac{8 π}{18}$

$= s i n^{2} \frac{π}{18} + s i n^{2} \frac{2 π}{18} + s i n^{2} (\frac{7 π}{18}) + s i n^{2} (\frac{8 π}{18})$

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

$(\frac{π}{2} - \frac{2 π}{18}) + s i n^{2} (\frac{π}{2} - \frac{8 π}{18})$

$= s i n^{2} \frac{π}{18} + s i n^{2} \frac{2 π}{18} + c o s^{2} \frac{2 π}{18} + c o s^{2} \frac{π}{18}$

$= s i n^{2} \frac{π}{18} + c o s^{2} \frac{π}{18} + s i n^{2} \frac{2 π}{18} + c o s^{2} \frac{2 π}{18}$

=1+1

=2

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Similar questions

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

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

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

. Find the value of

k

{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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sin2π18+sin2π9+sin27π18+sin24π9=

The correct option is C 2 2 We hav: sin2π18+sin2π9+sin27π18+sin24π9 =sin2π18+sin22π18+sin27π18+sin28π18 =sin2π18+sin22π18+sin2(7π18)+sin2(8π18) =sin2π18+sin22π18+sin2 (π2−2π18)+sin2(π2−8π18) =sin2π18+sin22π18+cos22π18+cos2π18 =sin2π18+cos2π18+sin22π18+cos22π18 =1+1 =2

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