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Prove that, sin(40^(@)+theta)cos(10^(@)+...

Prove that, `sin(40^(@)+theta)cos(10^(@)+theta)-cos(40^(@)+theta)sin(10^(@)+theta)=(1)/(2)`

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KUMAR PRAKASHAN-TRIGONOMETRIC FUNCTIONS -PRACTICE WORK
  1. Find the value of sin15^(@)

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  2. Find the value of sec105^(@)

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  3. Prove that, sin(40^(@)+theta)cos(10^(@)+theta)-cos(40^(@)+theta)sin(10...

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  4. Prove that, (tanA+tanB)/(tanA-tanB)=(sin(A+B))/(sin(A-B))

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  5. Prove that, cos^(2)45^(@)-sin^(2)15^(@)=sqrt(3)/(4)

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  6. Prove that, cos105^(@)+cos15^(@)=sin75^(@)-sin15^(@)

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  7. Prove that (tan69^(@)+tan66^(@))/(1-tan69^(@)tan66^(@))=-1

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  8. If sinA=(4)/(5)andcosB=(5)/(13), where 0ltA,Blt(pi)/(2) then find (i) ...

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  9. If x and y are acute angles and cosx=(13)/(14)andcosy=(1)/(7) then pro...

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  10. Prove that, sin^(2)((pi)/(8)+(A)/(2))-sin^(2)((pi)/(8)-(A)/(2))=(1)/...

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  11. Find the value of sin^(2)37(1^(@))/(2)-sin^(2)7(1)/(2)

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  12. Find the value of sin^(2)52(1^(@))/(2)-cos^(2)7(1^(@))/(2)

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  13. Find the value of cos^(2)37(1^(@))/(2)-sin^(2)37(1^(@))/(2)

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  14. Prove that, sin^(2)A+sin^(2)B+cos^(2)(A+B)+2sinAsinBcos(A+B)=1

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  15. Prove that sintheta+sin(theta+(2pi)/(3))+sin(theta+(4pi)/(3))=0

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  16. Prove that, cos20^(@)+cos60^(@)+cos100^(@)+cos140^(@)=(1)/(2)

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  17. Prove that, sin65^(@)+cos65^(@)=sqrt(2)cos20^(@)

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  18. Prove that, cos55^(@)+cos65^(@)+cos175^(@)=0

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  19. Prove that, (cos7A+cos5A)/(sin7A-sin5A)=cotA

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  20. Prove that, (sin""(5pi)/(12)-cos""(5pi)/(12))/(cos""(5pi)/(12)+sin""(5...

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