Prove - sin-11 7 - 8sin2-11 - -11-

sinπ11(7 8sin^2π11)=sinπ11( 1+8cos^2π11)=sinπ11( 1+4(1+cos2π11))=3sinπ11+4cos2π11sinπ11 #160; #160; #160; #160; #160; #160; #160; # ...

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Byju's Answer

Standard XII

Mathematics

Circular Measurement of Angle

prove : sinπ...

Question

prove :

$sin \frac{π}{11} (7 - 8 {sin}^{2} \frac{π}{11}) = \sqrt{11}$ .

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Solution

$sin \frac{π}{11} (7 - 8 {sin}^{2} \frac{π}{11}) = sin \frac{π}{11} (- 1 + 8 {cos}^{2} \frac{π}{11}) = sin \frac{π}{11} (- 1 + 4 (1 + cos \frac{2 π}{11})) = 3 sin \frac{π}{11} + 4 cos \frac{2 π}{11} sin \frac{π}{11}$
$= 3 sin \frac{π}{11} + 2 sin \frac{3 π}{11} + 2 sin \frac{π}{11} = 5 sin \frac{π}{11} + 2 sin \frac{3 π}{11} = \sqrt{11}$

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Similar questions

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sin (\frac{π}{6} + {cos}^{- 1} \frac{1}{4})

Q. Solve :-

sin (\frac{π}{2} - {sin}^{- 1} (\frac{1}{2}))

Match the column

$\begin{matrix} Column A & Column B 1.cos \frac{2 π}{7} + cos \frac{4 π}{7} + cos \frac{6 π}{7} & A.0 2.cos \frac{π}{7} + cos \frac{2 π}{7} +cos \frac{3 π}{7} + cos \frac{4 π}{7} + cos \frac{5 π}{7} + cos \frac{6 π}{7} & B. \frac{1}{2} 3.sin \frac{π}{11} + sin \frac{3 π}{11} + sin \frac{5 π}{11} + sin \frac{7 π}{11} + sin \frac{9 π}{11} & C. \frac{- 1}{2} \end{matrix}$

Q. Prove;

c o s \frac{π}{11} + c o s \frac{3 π}{11} + c o s \frac{5 π}{11} + c o s \frac{7 π}{11} + c o s \frac{9 π}{11} = \frac{1}{2}

Q. Using eular's formula prove that

\frac{c o s π}{11} + \frac{c o s 3 π}{11} + \frac{c o 5 π}{11} + \frac{c o s 7 π}{11} + \frac{c o s 9 π}{11} = \frac{1}{2} s i n x

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prove :sinπ11(7−8sin2π11)=√11.

sinπ11(7−8sin2π11)=sinπ11(−1+8cos2π11)=sinπ11(−1+4(1+cos2π11))=3sinπ11+4cos2π11sinπ11 =3sinπ11+2sin3π11+2sinπ11=5sinπ11+2sin3π11=√11

prove :

$sin \frac{π}{11} (7 - 8 {sin}^{2} \frac{π}{11}) = \sqrt{11}$ .