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Prove that: (1+cos. (pi)/8)(1+cos. (3pi...

Prove that: `(1+cos. (pi)/8)(1+cos. (3pi)/8)(1+cos. (5pi)/8)(1+cos. (7pi)/8)=1/8`

A

`1/2`

B

`cos""(pi)/(8)`

C

`1/8`

D

`(1+sqrt2)/(2sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS AND IDENTITIES-Exercise
  1. If tan(x/2)=cosec x-sin x, then find the value of tan^(2) (x/2).

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  2. If cosA=3/4, then 32 sin (A/2) sin ((5A) /2)= ------------- ...

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  3. Prove that: (1+cos. (pi)/8)(1+cos. (3pi)/8)(1+cos. (5pi)/8)(1+cos. (7...

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  4. If t a n^2theta=2t a n^2varphi+1 , prove that cos2theta+s in^2varphi=0...

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  5. If sin2theta=cos3thetaa n dtheta is an acute angle, then sintheta equa...

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  6. If f(x)=cos^2theta+sec^2theta, then f(x)<1 (b) f(x)=1 2>f(x)>1 (d)...

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  7. The value of sinpi/(14)sin(3pi)/(14)sin(5pi)/(14)sin(7pi)/(14)sin(9pi)...

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  8. The value of sin(pi/14)sin((3pi)/14)sin((5pi)/14) is

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  9. If sin(alpha+beta)=1\ a n dsin(alpha-beta)=1/2,\ w h e r e\ 0lt=,\ bet...

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  10. If cos(theta-alpha)=a and cos(theta-beta)=b then the value of sin^(2)(...

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  11. If K=sin(pi/(18))sin((5pi)/(18))sin((7pi)/(18)), then the numerical va...

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  12. Show that tan1^0tan2^0tan89^0=1

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  13. If 1+sinx+sin^2x+sin^3x+oo is equal to 4+2sqrt(3),0<x<pi, then x is eq...

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  14. If x cosalpha+y sinalpha=2a, x cos beta+y sinbeta=2aand 2sin""(alp...

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  15. If tan x =(2b)/ (a- c), y = acos^2 x + 2bsin x cos x + csin^2 x, z=as...

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  16. If alpha+beta+gamma=2pi, then show that tan.alpha/2 + tan.beta/2 + tan...

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  17. If sintheta-costhetalt0, then theta lies between

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  18. Within what limits must A/2 lies if 2sinA/2=-sqrt(1+sinA)-sqrt(1-sinA)...

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  19. If 2cos""(A)/(2)=sqrt(1+sinA)+sqrt(1-sinA), thenA/2 iles between,

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  20. Find the angle theta whose cosine is equal to its tangent.

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