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Prove that, 2(asin^(2)((C)/(2))+csin^(...

Prove that,
`2(asin^(2)((C)/(2))+csin^(2)((A)/(2)))=c+a-b`

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In triangle ABC, prove that, tan((B-C)/(2))=(b-c)/(b+c)cot((A)/(2)) tan((C-A)/(2))=(c-a)/(c+a)cot((B)/(2)) tan((A-B)/(2))=(a-b)/(a+b)cot((C)/(2))

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KUMAR PRAKASHAN-TRIGONOMETRIC FUNCTIONS -PRACTICE WORK
  1. For DeltaABC prove that, (a-b)^(2)cos^(2)""(C)/(2)+(a+b)^(2)sin^(2)"...

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  2. In DeltaABC,(sinA)/(sinC)=(sin(A-B))/(sin(B-C)) then prove that a^(2),...

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  3. Prove that, 2(asin^(2)((C)/(2))+csin^(2)((A)/(2)))=c+a-b

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  4. Prove that, tan((A)/(2)+B)=(c+b)/(c-b)tan((A)/(2))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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