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Prove that, sin^(2)A+sin^(2)B+cos^(2)(...

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

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KUMAR PRAKASHAN-TRIGONOMETRIC FUNCTIONS -PRACTICE WORK
  1. Find the value of sin^(2)52(1^(@))/(2)-cos^(2)7(1^(@))/(2)

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

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

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

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

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

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

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

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

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  10. Prove that, sin10^(@)+sin50^(@)-sin70^(@)=0

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  11. Prove that, cos18^(@)-sin18^(@)=sqrt(2)sin27^(@)

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  12. If sintheta=nsin(theta+2alpha) then prove that, tan(theta+alpha)=(1+n)...

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  13. Prove that, (cos3A+2cos5A+cos7A)/(cosA+2cos3A+cos5A)=cos2A-sin2A.tan3A

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  14. Prove that, sinA+sinB+sinC-sin(A+B+C)= 4sin((A+B)/(2))sin((B+C)/(2))...

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  15. Prove that, (cosA-cosB)^(2)+(sinA-sinB)^(2)=4sin^(2)((A-B)/(2))

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  16. Prove that, cos80^(@)+cos40^(@)-cos20^(@)=0

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  17. Prove that, sin51^(@)+cos81^(@)=cos21^(@)

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  18. Prove that, sinA+sin2A+sin4A+sin5A= 4cos((A)/(2))cos((3A)/(2))sin3...

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  19. Prove that, cos3A+cos5A+cos7A+cos15A=4cos4Acos5Acos6A.

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  20. Prove that, tan3A.tan2A.tanA=tan3A-tan2A-tanA

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