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If A + B + C =180^@, prove that : tan fr...

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

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

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) .

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

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

If A + B + C =pi , prove that : cos^2 frac (A)(2)+cos^2 frac (B)(2)-cos^2 frac (C)(2)= 2 cos frac (A)(2) cos frac (B)(2) sin frac (C)(2) .

Prove that : 1+tan A tan frac (A)(2)= secA= tanA cot frac (A)(2)-1

If A + B + C =pi , prove that : cos A+cos B+cos C=1+ 4 sin frac (A)(2) sin frac (B)(2) sin frac (C)(2) .

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) .

Prove that : (sinx)/(1+cos x)= tan frac (x)(2) .

If A + B + C =180^@ , prove that : sin (B + 2C) + sin (C + 2A) + sin (A + 2B) = 4 sin frac (B-C)(2) sin frac (C-A)(2) sin frac (A-B)(2) .

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. If A + B + C =360^@, prove that : 1-cos^2 A-cos^2 B-cos^2 C+2 cos A co...

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  2. If A + B + C =180^@, prove that : tan A + tan B + tan C = tan A tan B ...

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  3. If A + B + C =180^@, prove that : tan frac (A)(2) tan frac (B)(2)+ tan...

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  4. If A + B + C =180^@, prove that : tan 2A + tan 2B + tan 2C = tan 2A ta...

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  5. If A + B + C =pi/2, prove that : tan A tan B + tan B tanC +tanC tan A=...

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  6. If A + B + C =pi/2, prove that : cot A + cot B + cot C = cot A cot B c...

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  7. Find the values of the following : sin 48^@.

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  8. Find the values of the following : sin 23^@ 26'.

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  9. Find the values of the following : cos 20^@ 10’.

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  10. Find the values of the following : cos 16^@ 11’.

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  11. Find the values of the following : tan 54^@ 30’.

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  12. Find the values of the following : tan 42^@ 6’.

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  13. Find the values of the following : cot 131^@ 20’.

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  14. Find the values of the following : cot 46^@ 26’.

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  15. Find theta, 0< theta <90^@, if : sin theta = 0.7071.

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  16. Find theta, 0< theta <90^@, if : cos theta = 0.9604.

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  17. Find theta, 0< theta <90^@, if : tan theta = 34.37.

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  18. Find theta, 0< theta <90^@, if : cot theta = 3.018.

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  19. Find the angle whose sine is 0.6479.

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  20. Sketch the graphs of the following function : y=2 sin x.

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