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Prove that tan alpha+2 tan 2 alpha+2^(...

Prove that
`tan alpha+2 tan 2 alpha+2^(2)tan2^(2)alpha+..............+2^(n-1)tan2^(n-1)alpha+2^(n)cot2^nalpha=cotalpha`

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ALLEN-TRIGONOMETRIC RATIOS AND IDENTITIES-All Questions
  1. sum(r=1)^(n-1)cos^(2) (rpi)/2 is equal to

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  2. Prove that: (1+sec2theta)(1+sec4theta)(1+sec8theta)(1+sec2^ntheta)=t a...

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  3. Prove that tan alpha+2 tan 2 alpha+2^(2)tan2^(2)alpha+.................

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  4. S=cosecx+cosec 2x+cosec 4x+…+cosec 2nx=cot(x/2)−cot2nx

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  5. The expression (tan(x-(pi)/(2)).cos((3pi)/(2)+x)-sin^(3)((7pi)/(2)-x...

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  6. The values of cos^2 73^0+cos^2 47^0-sin^2 43^0+sin^2 107^0 is equal t...

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  7. The expression (sin 22^0cos8^0+cos 158^0cos98^0)/(sin 23^0cos7^0+cos 1...

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  8. The two legs of a right triangle are sin theta+sin((3pi)/(2)-theta) an...

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  9. If tantheta=sqrt(a/b)where a , b are positive reals then the value o...

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  10. The expression (sin(alpha+theta)-"sin"(alpha-theta))/(cos(beta-theta)-...

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  11. Exact value of cos 20^0+2sin^2\ \ 55^0-sqrt(2)sin65^0\ is- a.1 b. 1/(...

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  12. If cos(theta+phi)=mcos(theta-phi) ,then tantheta is equal to a.((1+m)...

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  13. If sin theta+"cosec"theta=2, then the value of sin^(8)theta+"cosec"^(...

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  14. If the expression 4sin5alphacos3alphacos2alpha s expressed as the su...

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  15. The expression 3[sin^4(3/2pi-alpha)+sin^4(3pi+alpha)]-2[sin^6(1/2pi+al...

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  16. If costheta=1/2(a+1/a)\ t h e n\ cos 3theta in term of ' a^(prime)= a...

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  17. The product cot123^0dotcot133^0dotcot137^0dotcot147^0, when simplified...

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  18. If A+B+C=pi\ &sin(A+C/2)=ksinC/2, t h e ntanA/2tanB/2= a.(k-1)/(k+1) ...

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  19. If alpha+beta+gamma=2pi, then tanalpha/2tanbeta/2+tangamma/2=tanalpha...

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  20. If A and C are two angles such that A+C=(3pi)/4 then (1+cotA)(1+cotC)=

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