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In any triangle ABC, prove that : cos f...

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

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

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) .

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 : a cos frac (B-C)(2)= (b +c) sin frac (A)(2)= (b+c)cos frac (B+C)(2) .

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 : sin (A + B) = sin C .

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

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

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

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove that : [1+ cot alpha- sec (pi/2+alpha)] [1+ cot alpha+ sec (pi/...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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