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If cot A= tan (n-1) A, show that one val...

If cot A= tan (n-1) A, show that one value of A is `pi/(2n)`.

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. In any triangle ABC, prove that : cos frac (A+B)(2)= sin frac (C)(2).

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

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  3. If cot A= tan (n-1) A, show that one value of A is pi/(2n).

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  4. Show that the function f(x) = cos 2x is periodic and find its period.

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  5. Show that the function f(x) = cos (x/2+pi/4) is periodic and find its ...

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  6. Evaluate : sin 15^@, cos 15^@, tan 15^@.

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  7. Evaluate : sin 75^@, cos 75^@, tan 75^@.

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  8. Prove that : sin 105^@ + cos 105^@=1/sqrt2.

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  9. Prove that : cos 105^@ + cos 15^@= sin 75^@- sin 15^@ .

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  10. Find tan 15^@ and hence show that tan 15^@+ cot 15^@ = 4.

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  11. Evaluate : sin^2 (15^@ + A) - sin^2 (15^@ -A).

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  12. Write down the values of : cos 68^@ cos 8^@ + sin 68^@ sin 8^@.

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  13. Write down the values of : cos 70^@ cos 10^@ + sin 70^@ sin 10^@.

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  14. Prove that : cos 130^@ cos 40^@+ sin 130^@ sin 40^@= 0.

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

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

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

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

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

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

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