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Prove that the value of each the followi...

Prove that the value of each the following determinants is zero: `|sin^2(x+(3pi)/2)sin^2(x+(5pi)/2)sin^2(x+(7pi)/2)sin^(x+(3pi)/2)sin^(x+(5pi)/2)sin^(x+(7pi)/2)sin^(x-(3pi)/2)sin^(x-(5pi)/2)sin^(x-(7pi)/2)|`

A

1

B

2

C

3

D

0

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The correct Answer is:
D
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Prove that the value of each the following determinants is zero: sin^(2)(x+(3 pi)/(2))quad sin^(2)(x+(5 pi)/(2))quad sin^(2)(x+(7 pi)/(2))sin(x+(3 pi)/(2))quad sin(x+(5 pi)/(2))quad sin(x+(7 pi)/(2))sin(x-(3 pi)/(2))quad sin(x-(5 pi)/(2))quad sin(x-(7 pi)/(2))

2sin((pi)/8)sin((2pi)/8)sin((3pi)/8)sin((5pi)/8)sin((6pi)/8)sin((7pi)/8) = ?

int_((-pi)/(2))^((pi)/(2))sin^(7)x dx

sin^(2)(pi)/(4)+sin^(2)(3 pi)/(4)+sin^(2)(5 pi)/(4)+sin^(2)(7 pi)/(4)=2

The value of 2 sin (pi/8) sin((2pi)/8) sin((3pi)/8) sin ((5pi)/8) sin ((6pi)/8) sin((7pi)/8) is :

int_(-pi//2)^(pi//2)sin^(7)x dx=

Prove that: sin^(2)pi/8+sin^(2)(3pi)/(8)+sin^(2)(5pi)/8+sin^(2)(7pi)/8=2

int_(-pi/2)^(pi/2) sin^(7) x dx

DISHA PUBLICATION-DETERMINANTS-EXERCISE -2 CONCEPT APPLICATOR
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  15. Prove that the value of each the following determinants is zero: |s...

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  19. If Delta(x)=|[sin2x, e^x sinx+x cosx, sinx+x^2 cosx] , [cosx+sinx, e^x...

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  20. Given that matrix A[(x,3,2),(1,y,4),(2,2,z)]. If xyz=60 and 8x+4y+3z=2...

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