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If tanx=(3)/(4),piltxlt(3pi)/(2), find t...

If `tanx=(3)/(4),piltxlt(3pi)/(2),` find the value of `sin""(x)/(2),cos""(x)/(2)` and `tan((x)/(2))`.

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The correct Answer is:
`(3)/(sqrt(10)),-(1)/(sqrt(10)),-3`
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KUMAR PRAKASHAN-TRIGONOMETRIC FUNCTIONS -TEXTBOOK ILLUSTRATIONS FOR PRACTICE WORK
  1. Show that, tan3xtan2xtanx=tan3x-tan2x-tanx.

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

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  3. Prove that, (cos7x+cos5x)/(sin7x-sin5x)=cotx

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  4. Prove that, (sin5x-2sin3x+sinx)/(cos5x-cosx)=tanx

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  5. Find the principal solutions of the equation sinx=sqrt(3)/(2).

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  6. Find the principal solutions of the equation tanx=-(1)/(sqrt(3)).

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  7. Find the solution of sinx=-(sqrt(3))/(2).

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  8. Solve cosx=(1)/(2).

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  9. Solve tan2x=-cot(x+(pi)/(3)).

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  10. Solve sin2x-sin4x+sin6x=0.

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  11. Solve 2cos^(2)x+3sinx=0.

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  12. In triangle ABC, prove that, tan((B-C)/(2))=(b-c)/(b+c)cot((A)/(2)) ...

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  13. In any triangle ABC, prove that asin(B-C)+bsin(C-A)+csin(A-B)=0.

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  14. The angle of elevation of the top point P of the vartical tower PQ of ...

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  15. A lamp post is situated at the middle point M of the side AC of a tria...

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  16. If sinx=(3)/(5),cosy=-(12)/(13), where x and y both lie in second quad...

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  17. Prove that, cos2xcos""(x)/(2)-cos3xcos""(9x)/(2)=sin5xsin""(5x)/(2).

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  18. Find the value of tan""(pi)/(8).

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  19. If tanx=(3)/(4),piltxlt(3pi)/(2), find the value of sin""(x)/(2),cos""...

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  20. Prove that, cos^(2)x+cos^(2)(x+(pi)/(3))+cos^(2)(x-(pi)/(3))=(3)/(2)...

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