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Prove the following: cot x cot 2x -cot 2...

Prove the following: `cot x cot 2x -cot 2x cot 3x -cot 3x cot x = 1`

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove that : tan 69^@ + tan 66^@+ 1 = tan 69^@ tan 66^@.

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  2. Prove that : (cos13^@+sin13^@)/(cos13^@-sin13^@) =tan 58^@.

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  3. Prove the following: cot x cot 2x -cot 2x cot 3x -cot 3x cot x = 1

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  4. Prove that : tan 3A - tan 2A - tan A = tan 3A tan 2A tan A.

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  5. Prove that : tan 7A -tan 5A-tan 2 A = tan 7A tan 5A tan 2A.

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  6. Prove that : tan 13A-tan 9A- tan 4A= tan 13A tan 9A tan 4A.

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  7. If cos (alpha+beta) sin (gamma+delta)=cos (alpha-beta) sin (gamma-delt...

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

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  9. If cot alpha cot beta=2, show that (cos (alpha+beta))/(cos (alpha-beta...

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  10. Prove that : tan 50^@ = tan 40^@ + 2 tan 10^@ .

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  11. Prove that : 2 tan 70^@ = tan 80^@ - tan 10^@.

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  12. If cos A=5/13 and sin B= 4/5 , find sin (A + B), where A, B, (A + B) ...

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  13. If tan x= a/(a+1) and tan y=1/(2a+1), show that one of the values of :...

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  14. In any quadrilateral ABCD, show that : cos A cos B - cos C cos D = si...

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  15. Prove that : cos theta- sin theta= sqrt2 cos (theta+ pi/4).

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  16. Prove that : tan (x-y)+tan (y -z) + tan (z-x)= tan (x-y)tan (y -z) t...

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  17. Prove that : cos^2 (pi/8+x/2)-sin^2 (pi/8-x/2)= 1/sqrt2 cos x.

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  18. Prove that : (cos^2 33^@- cos^2 57^@)/(sin^2 frac (21^@) (2)- sin^2 fr...

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  19. Find a and b such that a le3 cos theta +5 sin (theta-pi/6)le b holds ...

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  20. If sin alpha=15/17 and cos beta=12/13, find the values of : sin (alpha...

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