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Prove the following: sin (n + 1)x sin (n...

Prove the following: `sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x`

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove that : cos 130^@ cos 40^@+ sin 130^@ sin 40^@= 0.

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  2. Prove that : sin (40^@+theta)cos (10^@+theta)-cos (40^@+theta) sin (10...

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  3. Prove the following: sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n +...

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  4. Prove that (sin(x+y))/(sin(x-y))=(tanx+tany)/(tanx-tany)

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  5. Prove that (sin(x+y))/(sin(x-y))=(tanx+tany)/(tanx-tany)

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  6. Evaluate : tan frac (13 pi)(12).

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  7. Find the maximum and minimum values of : 15 cos theta-8 sin theta.

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  8. Prove that (sin(B-C))/(cos B cos C)+(sin(C-A))/(cos C cos A)+(sin(A-B)...

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  9. If cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2 , prove that ...

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  10. If theta+phi=45^@, prove that (cot theta-1) (cot phi-1) =2.

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  11. If theta - phi=pi/4, prove that : (1 + tan theta)(1-tan phi)=2.

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  12. If theta - phi=pi/4, prove that : (1 + tan theta)(1+tan phi)=2 tan ...

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  13. Prove that : tan 69^@ + tan 66^@+ 1 = tan 69^@ tan 66^@.

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

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

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

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

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

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

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

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