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

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

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(cos x + cos y ) ^(2) + (sin x - sin y ) ^(2) = 4 cos ^(2) ""(x + y )/( 2)

cos ^(-1) ""((cos x + cos y)/(1+cos x cos y))= 2 tan ^(-1) (tan ""(x)/(2) tan ""(y)/(2))

(cos x- cos y) ^(2) + (sin x - sin y) ^(2) =4 sin ^(2) "" ( x-y)/(2)

Prove that, cos 4 x - cos4 y = 8(cos x - cos y)(cos x + cos y)(cos x - sin x)(cos x + sin y)

If y= tan^(-1)((a cos x-b sin x)/(b cos x+a sin x))" show that, " (dy)/(dx)= -1 .

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NCERT BANGLISH-TRIGONOMETRIC FUNCTIONS -EXERCISE 3.3
  1. 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. cos ((3pi )/( 2 ) + x) cos (2pi + x) [cot ((3pi)/( 2)- x ) + cot (2pi ...

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  5. sin (n +1) x sin (n +2) x + cos (n +1) x cos (n +2) x = cos x

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  6. cos ((3pi)/( 4) + x) - cos((3pi)/( 4) -x) =- sqrt2 sin x

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  7. sin ^(2) 6x - sin ^(2) 4x = sin 2x sin 10x

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

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

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

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  11. (cos 9x - cos 5x )/( sin 17 x- 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. (sin x - sin 3x)/( sin ^(2) x - cos ^(2) x) = 2 sin x

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

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

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  18. tan 4x = (4 tan x (1- tan ^(2) x ))/( 1 - 6 tan ^(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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