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Prove that : cos C +cosD = 2 cos frac (...

Prove that :
`cos C +cosD = 2 cos frac (C+D)(2) cos frac (C-D) (2)` .

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Prove that : sinC +sinD =2 sin frac (C+D)(2) cos frac (C-D) (2) .

Prove that : sinC-sinD = 2 cos frac (C+D)(2) sin frac (C-D) (2) .

Prove that : cosC-cosD = 2sin frac (C+D)(2) sin frac (D-C) (2) .

If A + B + C =pi , prove that : cos A+cos B - cos C= 4 cos frac (A)(2) cos frac (B)(2) sin frac (C)(2)-1 .

If A + B + C =pi , prove that : . sin A + sin B+sinC = 4 cos frac (A)(2) cos frac (B)(2) cos frac (C)(2) .

In any triangle ABC, prove that : cos frac (A)(2) +cos frac (B)(2)+cos frac (C)(2)= 4 cos frac (pi-A)(4) cos frac (pi-B)(4) cos frac (pi-C)(4) .

If A + B + C =pi , prove that : cos A+cos B+cos C=1+ 4 sin frac (A)(2) sin frac (B)(2) sin frac (C)(2) .

If A + B + C =pi , prove that : (sin 2A + sin 2B + sin 2C)/(cos A + cos B + cos C-1)= 8 cos frac (A)(2) cos frac (B)(2) cos frac (C)(2) .

If A+B +C +D= 2 pi , prove that : cos A + cos B + cos C + cos D =-4 cos frac (A+B)(2) cos frac (A+C)(2) cos frac (A+D)(2) .

If A + B + C =pi , prove that : cos^2 frac (A)(2)+cos^2 frac (B)(2)-cos^2 frac (C)(2)= 2 cos frac (A)(2) cos frac (B)(2) sin frac (C)(2) .

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove that : cos C +cosD = 2 cos frac (C+D)(2) cos frac (C-D) (2) .

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  2. Find the radian measure corresponding to the following degree measure ...

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  3. Find the radian measure corresponding to the following degree measure ...

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  4. Find the radian measure corresponding to the following degree measure ...

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  5. Find the radian measures corresponding to the following degree measure...

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  6. Find the radian measure corresponding to the following grade measure :...

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  7. Find the radian measure corresponding to the following grade measure :...

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  8. Find the radian measure corresponding to the following grade measure :...

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  9. Find thedegree measure corresponding to the following measure. (Use pi...

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  10. Find thedegree measure corresponding to the following measure. (Use pi...

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  11. Find thedegree measure corresponding to the following measure. (Use pi...

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  12. Find thedegree measure corresponding to the following measure. (Use pi...

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  13. The angles of a triangle are3x^@, ((4x)/3)^g and (2 pi x)/75 radians. ...

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  14. Express the radians the fourth angle of a quadrilateral which has thre...

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  15. The sum of two angles is 80 grades and their difference is 18^@. Find ...

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  16. The angles of a triangle are in the ratio 1 : 2: 3. Find the angles in...

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  17. The vertical angle of an isosceles triangle is 2/3 rd of each of its b...

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  18. In a right-angled triangle, the difference between two acute angles is...

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  19. The wheel of a carriage is 91 cm in diameter and makes 5 revolutions p...

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  20. A wheel makes 360 revolutions in one minute. Through how many radians ...

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  21. Find the length of the arc of a circle of radius 5 cm subtending an an...

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