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Solve : 4costheta-3sectheta=tantheta...

Solve : `4costheta-3sectheta=tantheta`

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Verified by Experts

The correct Answer is:
`npi+(-1)^(n)alpha`, where `sinalpha=(-1+sqrt(17))/(8),ninZ`
`npi+(-1)^(n)beta,` where `sinbeta=(-1-sqrt(17))/(8),ninZ`
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Prove the following identities. where the angles involved are acute angles for which the expressions are defined. (sintheta-2sin^(3)theta)/(2cos^(3)theta-costheta)=tantheta

If theta_(1),theta_(2),theta_(3),".......",theta_(n) are in AP whose common difference is d, then show that sind{sectheta_(1) sectheta_(2)+ sectheta_(2)sectheta_(3)+"........"+sectheta_(n-1)sectheta_(n)}=tantheta_(n)-tantheta_(1) .

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KUMAR PRAKASHAN-TRIGONOMETRIC FUNCTIONS -PRACTICE WORK
  1. Prove that, tan((A)/(2)+B)=(c+b)/(c-b)tan((A)/(2))

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  2. Prove that, a^(3)sin(B-C)+b^(3)sin(C-A)+c^(3)sin(A-B)=0

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

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

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  5. Prove that, 4sin27^(@)=sqrt(5+sqrt(5))+sqrt(3-sqrt(5))

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  6. If alpha and beta are roots of the equation acostheta+bsintheta=c then...

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  7. If alpha and beta are roots of the equation acostheta+bsintheta=c then...

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  8. If costheta=a then show that cos^(2)((theta)/(2)) and sin^(2)((theta)/...

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  9. Prove that, (2costheta+1)(2costheta-1) (2cos2theta-1)(2cos4theta-1)=...

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  10. If DeltaABC is a right angle triangle then prove that cos^(2)A+cos^(2)...

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  11. If cosalpha=(3)/(5),cosbeta=(5)/(13),0ltalpha,betalt(pi)/(2) then find...

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  12. Prove, sin6^(@).sin(42^(@)).sin(66^(@)).sin(78^(@))=(1)/(16) .

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  13. Prove that 2tanbeta+cotbeta=tanalphaimplies2tan(alpha-beta)=cotbeta.

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  14. If theta+beta=alphaandsintheta=ksinbeta then prove that tantheta=(ksin...

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  15. If asintheta=bsin(theta+(2pi)/(3))=csin(theta+(4pi)/(3)) then prove th...

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  16. If cosalpha=(-5)/(13),(pi)/(2)ltalphaltpiandtanbeta=(4)/(3),piltbetalt...

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  17. Solve : sqrt(2)sectheta+tantheta=1

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  18. Solve : 4costheta-3sectheta=tantheta

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  19. If costheta=(cosalphacosbeta)/(1-sinalphasinbeta) then prove that ta...

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  20. If tanA=(1)/(7) and tanB=(1)/(3) then show that cos(2A)=sin(4B).

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