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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`

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To prove that \[ (1 + \cos(\frac{\pi}{8}))(1 + \cos(\frac{3\pi}{8}))(1 + \cos(\frac{5\pi}{8}))(1 + \cos(\frac{7\pi}{8})) = \frac{1}{8} \] we will follow these steps: ...
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cos^2(pi/8) +cos^2((3pi)/8) +cos^2((5pi)/8)+cos^2 ((7pi)/8)=2

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove that:(sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

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  2. Prove that: (cosA+cosB)^2+(sinA-sinB)^2=4cos^2((A+B)/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 sinA=3/5, where 0^0ltAlt90^0 , then find the values of sin2A , cos2...

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  5. Prove that: sin(pi/10) sin((13pi)/10)=-1/4

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  6. Show that: sqrt(2+sqrt(2+sqrt(2+2cos8theta)))=2costheta,0<theta<pi 8<=...

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  7. If tanalpha=1/7,sinbeta=1/(sqrt(10)), prove thatalpha+2beta=pi/4 , whe...

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  8. If tan(pi/4+theta/2)=tan^3(pi/4+alpha/2) then sin(theta)=(sin(alpha)(...

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  9. If sin(theta+alpha)=a, a n dsin(theta+beta)=b , prove that cos2(alpha-...

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  10. Prove that: t a nalpha+2tan2alpha+4tan4alpha+8cot8alpha=cotalpha

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  11. If t a nalpha=p/q , where alpha=6beta,alpha being acute angle, prove...

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  12. If costheta=cosalphacosbeta , prove that t a n(theta+alpha)/2t a n(th...

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  13. If t a ntheta/2=sqrt((a-b)/(a+b))tanvarphi/2 , prove that costheta=(a ...

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  14. Prove that: (2cos2^ntheta+1)/(2costheta+1)=(2costheta-1)(2cos2theta-1)...

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  15. If t a ntheta/2=sqrt((a-b)/(a+b))tanvarphi/2 , prove that costheta=(a ...

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  16. Prove that: sin3e sin^3e+cos3ecos^3e=cos^3 2e

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  17. If cosalpha+cosbeta+cosgamma=0 , then prove that cos3alpha+cos3beta+co...

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  18. If costheta=(cosalpha cosbeta)/(1-sinalphasinbeta) , prove that one va...

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  19. If costheta=(cosalpha-cosbeta)/(1-cosalpha.cosbeta) , prove that t a ...

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  20. sin5A=5cos^4AsinA-10cos^2Asin^3A+sin^5A

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