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sin^(2)pi/8+sin^(2)(3pi)/(8)+sin^(2)(5pi...

`sin^(2)pi/8+sin^(2)(3pi)/(8)+sin^(2)(5pi)/(8)+sin^(2)(7pi)/(8)=?`

A

`-1`

B

1

C

`-2`

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
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Prove that: cos^(2)pi/8 + cos^(2)(3pi)/(8) + cos^(2)(5pi)/(8)+ cos^(2)(7pi)/(8)=2

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

(cos^(2)pi)/(8)+(sin^(2)(3 pi))/(8)+(sin^(2)(5 pi))/(8_(sin)^(2))(7 pi)/(8)=2

Prove that: sin^(4)((pi)/(8))+sin^(4)((3 pi)/(8))+sin^(4)((5 pi)/(8))+sin^(4)((7 pi)/(8))=(3)/(2)

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

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

The value of sin^(4)(pi/8)+cos^(4)((3 pi)/8)+sin^(4)((5pi)/8)+cos^(4)((7pi)/8) is equal to =

Prove that sin^(4) pi/8+ sin^(4) 3pi/8 + sin^(4) 5pi/8 + sin^(4) 7pi/8 = 3/2 .

Statement I : sin^2pi/8+sin^2(3pi)/8+sin^2(5pi)/8+sin^2(7pi)/8=2 Statement II cos^2pi/8+cos^2(3pi )/8+cos^2(5pi)/8+cos^2(7pi/8)=2 Statement III: sin^2pi/8+sin^(3pi)/8+sin^2(5pi)/8sin^2 (7pi)/8=3/2

NAGEEN PRAKASHAN-TRIGNOMETRIC FUNCTIONS-EXERCISES 3P
  1. If 2costheta=x+1/x, then 2cos2theta=?

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  2. If A+B=45^@ then (1+tanA)(1+tanB)=

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  3. sin^(2)pi/8+sin^(2)(3pi)/(8)+sin^(2)(5pi)/(8)+sin^(2)(7pi)/(8)=?

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  4. If sinx+sin^(2)x=1 ,then cos^(4)x+cos^(2)x=?

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  5. If 4sin^(2)theta=3, then general value of theta is:

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  6. If sin7theta=cos5 theta, then general value of theta is:

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  7. If tan3theta=cottheta, then general value of theta is :

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  8. Find the general value of theta from the equation tantheta+tan2theta+t...

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  9. The solution of tantheta+cottheta=2 is:

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  10. The solution of cos2theta=cos^(2)theta is:

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  11. cottheta=-sqrt(3) and cosec theta=2

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  12. Solve: 2sin^(2)theta+sin^(2)2theta=2

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  13. If sqrt(3)sintheta-costheta=0, then one general value of theta is:

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  14. In DeltaABC, a=12 m, angleB=30^(@) and angleC=90^(@), then area of Del...

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  15. In DeltaABC, a=12 cm, angleB=30^(@) and angleC=90^(@), then area of De...

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  16. In DeltaABC, cotA/2, cotB/2, cotC/2 are in A.P., then the true stateme...

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  17. If a, b, c are in A.P then cot(A/2),cot(B/2),cot(C/2) are in

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  18. In DeltaABC, a=9, b=8 and c=4, then 3cosB-6cosC=?

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  19. In DeltaABC, If 1/(a+b)+1/(b+c)=3/(a+b+c), then angleB=?

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  20. Prove that in triangleABC, a^3cos(B-C)+b^3cos(C-A)+c^3cos(A-B)=3abc

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