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If A, B, C and D be the angles of a cycl...

If A, B, C and D be the angles of a cyclic quadrilateral, taken in order, prove that : `cos (180^@- A) + cos (180^@+ B) + cos (180^@+ C)- sin (90^@ + D) = 0`.

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Find the period of the following function: cos 3x.

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  2. Find the period of the following function: tan 2x.

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  3. If A, B, C and D be the angles of a cyclic quadrilateral, taken in ord...

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  4. If x=(11 pi)/4, prove that : sin^2 x- cos^2 x+2 tan x- sec^2 x=1.

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  5. If 8 theta=pi, prove that cos theta+ cos 7 theta=0.

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  6. If B + C = 60^@, show that : sin (120^@- B) = sin (120^@ -C) .

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  7. Prove that : sin^2 frac (pi)(8)+ sin^2 frac (3pi)(8)+ sin^2 frac (5pi)...

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  8. Prove that : [1+ cot alpha- sec (pi/2+alpha)] [1+ cot alpha+ sec (pi/...

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

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

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

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

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

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

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

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

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

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

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

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

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