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Prove the following: cos((3pi)/2+x)cos(2...

Prove the following: `cos((3pi)/2+x)cos(2pi+x)[cot((3pi)/2-x)+cot(2pi+x)]=1`

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove that : 3 sin frac (pi)(6) sec frac (pi)(3)-4 sin frac (5pi)(6) c...

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  2. Prove that : (cos(pi+theta)cos(-theta))/(sin (pi-theta) cos (pi/2+ the...

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  3. Prove the following: cos((3pi)/2+x)cos(2pi+x)[cot((3pi)/2-x)+cot(2pi+x...

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  4. Find ‘x’ from the equation : cosec (90^@ -theta) - x sin (90^@- theta)...

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  5. Find ‘x’ from the equation : cosec (90^@ -theta) - x sin (90^@- theta)...

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  6. In any quadrilateral ABCD, prove that: sin (A + B) + sin(C +D)=0.

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  7. Find all the values of theta satisfying 0lt theta lt pi and tan^2 the...

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  8. Find the period of the following function: sin 2x.

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  9. Find the period of the following function: cos 3x.

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

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

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

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

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

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

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

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

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

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

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

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