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4 sin (420^(@) - alpha ) cos (60^@ + alp...

`4 sin (420^(@) - alpha ) cos (60^@ + alpha ) = `

A

`sqrt(3) + 2 sin 2 alpha `

B

` sqrt(3)-2 sin 2 alpha `

C

`sqrt(3)+2 cos 2 alpha `

D

`sqrt(3) -2 cos 2 alpha `

Text Solution

Verified by Experts

The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 D ( TRANSFORMATIONS )
  1. cos^(2) ( 45^(@) - alpha ) + cos^(2) (15^(@) + alpha ) - cos^(2)(15^(@...

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  2. 2 cos theta - cos 3 theta - cos 5 theta - 16 cos^(3) theta sin^(2) the...

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  3. 4 sin (420^(@) - alpha ) cos (60^@ + alpha ) =

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  4. ( sin A + sin 5A + sin 9A)/( cos A + cos 5A + cos 9A)=

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  5. ( sin 2 theta + 2 sin 4 theta + sin 6 theta )/(sin 4 theta + 2 sin 6 t...

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  6. ( cos 6 x + 6 cos 4 x+ 15 cos 2 x+ 10)/( cos 5 x+ 5 cos 3 x + 10 cos ...

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  7. ( cos A + cos 3A + cos 5A + cos 7A )/( sin A + sin 3A + sin 5A + sin 7...

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  8. If none of A,B, A+B is an integral multiple of pi, then prove that (1-...

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  9. ( sin(n+1) alpha - sin (n-1)alpha )/( cos (n+1) alpha + 2 cos n alpha ...

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  10. ((cos theta - cos 3 theta ) ( sin 8 theta + sin 2 theta ))/(( sin 5 th...

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  11. ( sin 8 alpha * cos alpha - sin 6 alpha * cos 3 alpha )/(cos 2 alpha c...

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  12. ( sin alpha sin 3alpha + sin 3alpha sin 7 alpha + sin 5 alpha sin 15 ...

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  13. ( sin 4 A sin 3A - sin 5A sin 2A+ sin 7A sin 4A )/(cos 2A cos 3A - cos...

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  14. (sin 65^(@) + sin 25^(@))/( cos 65^(@) + cos 25^(@))=

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  15. ( sin 70^(@) + cos 40^(@) )/( cos 70^(@) + sin 40^(@))=

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  16. ( sin 75^(@) - sin 15^(@))/( cos 15^(@) - cos 75^(@))=

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  17. ( cos^(2) 33^(@) - cos^(2) 57^@)/( sin 21^(@) - cos 21^(@))=

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  18. (1+ cos 56^(@) + cos 58^(@) - cos 66^(@))/( cos 28^(@) cos 29^@ sin 3...

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  19. ( cos (45^(@) + A) - cos (45^(@) - A))/( sin (120^(@) + A)-sin(120^@-A...

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  20. A+C=2B implies ( cos C - cos A )/( sin A - sin C )=

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