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Prove that: sin(8pi)/3cos(23pi)/6+cos(13...

Prove that: `sin(8pi)/3cos(23pi)/6+cos(13pi)/3sin(35pi)/6=1/2`

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Consider LHS
`sin(8pi)/3cos(23pi)/6+cos(13pi)/3sin(35pi)/6`
`=sin 480° * cos 690° + cos 780° * sin 1050°`
`=sin (90° × 5 + 30°) * cos (90° × 7 + 60°) + cos (90° × 8 + 60°) * sin (90° × 11 + 60°)`
As we know that when n is odd, sin → cos and cos → sin
Therefore LHS
`= cos 30° sin 60° + cos 60° [-cos 60°]`
`=sqrt 3/2 xx sqrt 3/2 - 1/2 xx 1/2`
`=3/4 - 1/4` ...
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RD SHARMA-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Find the values of the following trigonometric ratio: sin1845^0

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  2. Prove that: t a n 225^0cot 405^0+t a n 765^0cot 675^0=\ 0

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  3. Prove that: sin(8pi)/3cos(23pi)/6+cos(13pi)/3sin(35pi)/6=1/2

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  4. Prove that: cos 24^0+cos55^0+cos 125^0+cos 204^@+cos 300^0=1/2

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  5. Prove that: tan(-225^0)cot(-405^0)-tan(-765^0)cot(675^0)=0

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  6. Prove that:cos 570^0sin510^0+sin(-330^0)cos(-390^0)=0

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  7. tan((11pi)/3)-2sin((9pi)/3)-3/4cosec^2(pi/4)+4cos^2((17pi)/6)=(3-2sqrt...

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  8. Prove that: 3sin(pi/6)sec(pi/3)-4sin((5pi)/6)cot(pi/4)=1

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  9. In a DeltaA B C prove that cos(A+B)+cos C=0.

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  10. In a Delta(ABC) prove that cos(("A"+"B")/2)=sin"C"/2dot

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  11. In a "DeltaA B C prove that tan(("A"+"B")/2)=cot("C"/2)

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  12. If A ,\ B ,\ C ,\ D be the angles of a cyclic quadrilateral, taken in ...

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  13. Find x from the following equation: cos e c(90^@+theta)+x costhetacot(...

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  14. Find x from the following equation: xcot(90^0+theta)+tan(90^0+theta)si...

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  15. Prove that: t a n 720^0-cos 270^0-s in 150^0cos 120^0=1/4

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  16. Prove that: sin 780^0sin 480^0+cos 120^0sin 150^0=1/2

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  17. Prove that: sin780^0sin 120^0+cos 240^0sin390^0=1/2

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  18. Prove that: sin600^0cos 390^0+cos 480^0sin 150^0=-1

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  19. tan 225^@ cot 405^@+ tan 765^@ cot 675^@=0

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  20. Write the maximum and minimum values of cos(cosx)

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