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

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

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. The value of (cos3theta)/(2cos2theta-1) is equal to (a) costheta (b) ...

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

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

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

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  5. Prove that: (1+cos4x)/(cot x-tanx)=1/2sin4x

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  6. Prove that: (cos7x-cos8x)/(1+2cos5x)=cos2x-cos3x

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  7. To prove (cos5x+cos4x)/(1-2cos3x)=-cos2x-cosx

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  8. If tantheta= t, then tan2theta+sec2theta is equal to (a) (1+t)...

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  9. Prove that: "cot"pi/(24)=sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6)

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  10. (sec8A-1)/(sec4A-1) is equal to (A) (tan2A)/(tan8A) (B) (tan8A)/(t...

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  11. If A=2sin^2theta-cos2theta,t h e nA lies in the interval (a) [-1,3] (...

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  12. Prove that (tan3x)/(tanx) never lies between 1/3a n d3 .

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  13. The value of (cot (x/2)-t a n (x/2))^2(1-2tanxcot2x) is (a)1 (b) 2 (c)...

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  14. Prove that cos^3A+cos^3(120^0+A)+cos^3(240^0+A)=3/4cos3A

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  15. Simplify 2sin^2beta+4cos(alpha+beta)sinalphasinbeta+cos2(alpha+beta)

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  16. Prove that: "tan"pi/(16)=sqrt(4+2sqrt(2))-(sqrt(2)+1)

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  17. Prove that: "tan"142""(1^0)/2=2+sqrt(2)-sqrt(3)-sqrt(6)

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  18. Prove that:(sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

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  19. Prove that: (cosA+cosB)^2+(sinA-sinB)^2=4cos^2((A+B)/2) .

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

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