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Prove that: sin^2(A/2+pi/8) - sin^2(A/2-...

Prove that: `sin^2(A/2+pi/8) - sin^2(A/2-pi/8)= 1/sqrt(2)sinA`

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove that: cos(pi/7)cos((2pi)/7)cos((4pi)/7)=-1/8

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  2. If alpha and beta are distinct roots of acostheta+b sintheta=c , prove...

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  3. Prove that: sin^2(A/2+pi/8) - sin^2(A/2-pi/8)= 1/sqrt(2)sinA

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  4. Prove that: Sin 4A = 4 cos^3 A sin A - 4 sin^3 A cos A

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  5. If tanA=1/7a n d tanB=1/3 , show that cos2A=sin4Bdot

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  6. If 2t a nalpha/2=tan(beta/2) , prove that cosalpha=(3+5cosbeta)/(5+3c...

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  7. If acos2theta+bsin2theta= c, alpha and beta as its roots , then prove ...

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  8. If cosalpha+cosbeta=0=s inalpha+s inbeta, then prove that cos2alpha+co...

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  9. Prove that: 15sin(5pi)/(12)+15cos(5pi)/(12)-20sin^3(5pi)/(12)-20cos(5p...

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  10. Prove that: sin(pi/5)sin( (2pi)/5)sin(3pi/5)sin(4pi/5)=5/(16)

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  11. Find general solution of the trigonometric equation sin5theta =1

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

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

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  14. Prove that:tan6^0tan42^0tan66^0tan78^0=1.

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  15. If tanalpha=(1-cosbeta)/(sinbeta),t h e n (a)tan3alpha=tan2beta (b) ...

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  16. Prove that: sin36^0=(sqrt(10-2sqrt(5)))/4 .

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  17. The value of (cos3theta)/(2cos2theta-1) is equal to (a) costheta (b) ...

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  18. The value of cos^4theta+sin^4theta-6cos^2theta is (a) cos2theta (b) s...

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  19. Prove that: sin(pi/10)+sin((13pi)/10)=-1/2

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  20. If tan(pi//4+theta)+""tan(pi//4-theta)=lambdasec2theta,t h e nlambda= ...

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