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In any triangle ABC, prove that : sin ...

In any triangle ABC, prove that :
`sin frac (A)(2) +sin frac (B)(2)+sin frac (C)(2)=1+4 sin frac (pi-A)(4) sin frac (pi-B)(4) sin frac (pi-C)(4)`.

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In any triangle ABC, prove that : cos frac (A+B)(2)= sin frac (C)(2) .

In any triangle ABC, prove that : cos frac (A)(2) +cos frac (B)(2)+cos frac (C)(2)= 4 cos frac (pi-A)(4) cos frac (pi-B)(4) cos frac (pi-C)(4) .

In any triangle ABC, prove that : sin frac (A-B)(2)= (a-b)/c cos frac (C)(2) .

In any triangle ABC, prove that : a sin (A/2+B)= (b +c) sin frac (A)(2) .

In any triangle ABC, prove that : tan frac (B+C-A)(2)= cot A .

If A + B + C =180^@ , prove that : sin^2 frac (A)(2)+ sin^2 frac (B)(2)+sin^2 frac (C)(2)=1-2 sin frac (A)(2)sin frac (B)(2)sin frac (C)(2) .

In any triangle ABC, prove that : sin frac (B-C)(2) = (b-c)/(a) cos frac (A)(2) .

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

In any triangle ABC, prove that : (a-b)/c= (sin frac (A-B)(2))/(cos frac (C)(2)) .

In any triangle ABC, prove that : cos frac (B-C)(2)= 2 sin frac (A)(2) , when b+c=2a .

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. If theta(1),theta(2),theta(3),".......",theta(n) are in AP whose commo...

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  2. If A + B + C =pi, prove that : cos 4A + cos 4B + cos 4C =-1+4 cos 2A c...

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  3. In any triangle ABC, prove that : sin frac (A)(2) +sin frac (B)(2)+s...

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  4. In any triangle ABC, prove that : cos frac (A)(2) +cos frac (B)(2)+c...

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  5. If A + B + C =180^@, prove that : sin (B+C-A) + sin(C+ A-B)+ sin(A +B-...

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  6. If A + B + C =180^@, prove that : cos (-A+B +C)+cos(A-B+C)+ cos (A +B-...

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  7. If A + B + C =180^@, prove that : sin (B+C-A) + sin(C+ A-B)+ sin(A +B-...

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  8. If in triangle ABC, cot A + cot B + cot C = sqrt3, prove that the tria...

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  9. If A+B +C +D= 2 pi, prove that : cos A + cos B + cos C + cos D =-4 cos...

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  10. If A+B +C =2S, prove that : sin (S - A) + sin (S- B) + sin (S-C)-sinS=...

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  11. If A+B +C =2S, prove that : cos^2 S + cos^2 (S- A) + cos^2 (S-B)+ cos^...

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  12. If x +y+ z=xyz, prove that : (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)= ...

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  13. If x +y+ z=xyz, prove that : (3x-x^3)/(1-3x^2)+ (3y-y^3)/(1-3y^2)+(3z...

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  14. If xy + yz + zx = 1, prove that : x/(1-x^2)+y/(1-y^2)+z/(1-z^2)= (4xy...

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  15. Find the solutions x in [0,2 pi] of : sin 2x-12 (sin x -cos x) + 12 =...

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  16. Solve the following trigonometric equation : cos 3 theta + 8cos^3 th...

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  17. If tan(pi cos theta )= cot (pi sin theta ) ,then cos^(2)(theta -pi/...

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  18. Find all the solution of 4 cos^(2)x sinx -2 sin^(2) x=3 sinx

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  19. In any triangle ABC, prove that : (b^2-c^2)/(a^2)= sin (B -C)/sin(B+C)...

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  20. Find the radian measure of the following degree measure 40°20

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