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Prove that sin(n+1)xsin(n+2)x+cos(n+1)...

Prove that
`sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx`

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NCERT GUJARATI-TRIGONOMETRIC FUNCTIONS -EXERCISE 3.3
  1. Prove that cos((pi)/(4)-x)cos((pi)/(4)-y)-sin((pi)/(4)-x)sin((pi)/(4...

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  2. (tan ((pi)/(4) +x))/( tan ((pi)/(4) -x ))= ((1 + tan x )/( 1- tan x ))...

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  3. (cos (pi +x) cos (-x))/( sin (pi -x) cos ((pi )/(2) + x))= cot ^(2) x

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  4. Prove that cos((3pi)/(2)+x)cos(2pi+x).{cot((3pi)/(2)-x)+cot(2pi+x)}=1

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  5. Prove that sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

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  6. Prove that, cos((pi)/(4)+x)+cos((pi)/(4)-x)=sqrt(2)cosx.

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  7. Prove that sin^(2)6x-sin^(2)4x=sin2xsin10x

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  8. cos ^(2) 2x -cos ^(2) 6x = sin 4x sin 8x

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  9. Prove that sin(2x)+2sin(4x)+sin(6x)=4cos^(2)xsin4x

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  10. cot 4x (sin 5x + sin 3x) = cot x (sin 5x - sin 3x)

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  11. Prove that (cos(9x)-cos(5x))/(sin(17x)-sin(3x))=-(sin(2x))/(cos(10x)...

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  12. (sin 5x + sin 3x )/( cos 5x + cos 3x ) = tan 4x

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  13. (sin x - sin y)/( cos x + cos y) = tan ""(x-y)/(2)

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  14. (sin x + sin 3x )/( cos x + cos 3x )= tan 2x

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  15. Prove that (sinx-sin3x)/(sin^(2)x-cos^(2)x)=2sinx

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  16. Prove that (cos(4x)+cos(3x)+cos(2x))/(sin(4x)+sin(3x)+sin(2x))=cot(3...

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  17. cot x cot 2x - cot 2x cot 3x - cot 3x cot x=1

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  18. Prove that tan4x=(4tanx(1-tan^(2)x))/(1-6tan^(2)x+tan^(4)x)

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  19. cos 4x =1- 8 sin ^(2) x cos ^(2) x

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  20. cos 6x = 32 cos ^(6) x - 48 cos ^(4) x + 18 cos ^(2) x-1

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