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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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PSEB-TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Prove the following: (tan(pi/4+x))/(tan(pi/4-x))=((1+tanx)/(1-tanx))^2

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  2. Prove the following: (cos(pi+x)cos(-x))/(sin (pi-x) cos(pi/2+x))=cot^2...

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

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  5. Prove the following: cos((3pi)/4+x)-cos((3pi)/4-x)=-sqrt2 sinx

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  6. Prove the following: sin^2 6x-sin^2 4x = sin 2x sin 10x

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  7. Prove the following: cos^2 2x - cos^2 6x = sin 4x sin 8x

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  8. Prove the following: sin2 x + 2 sin 4x + sin 6x = 4 cos^2 x sin 4x

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  9. Prove the following: cot 4x (sin 5x + sin 3x) = cot x (sin 5x -sin 3x)

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  10. Prove the following: (cos9x -cos5x)/(sin17x-sin3x)=-(sin2x)/(cos10x)

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  11. Prove the following: (sin5x + sin 3x)/(cos5x + cos3x)=tan4x

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  12. Prove the following: (sin x-sin y)/(cosx + cos y)=tanfrac(x-y)(2)

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  13. Prove the following: (sinx + sin3x)/(cosx + cos3x)=tan 2x

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  14. Prove the following: (sin x -sin 3x)/(sin^2 x -cos^2 x)= 2sinx

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  15. Prove the following: (cos4x + cos3x + cos2x)/(sin4x + sin 3x + sin 2x)...

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

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  17. Prove the following: tan 4x =(4tan x (1-tan^2x))/(1-6 tan^2x + tan^4x)

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  18. Prove the following: cos 4x = 1 - 8sin^2 x cos^2 x

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  19. Prove the following: cos 6x = 32 cos^6 x -48cos^4 x + 18 cos^2 x - 1

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  20. Find the principal and general solutions of the following equation:- t...

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