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Prove that, (cosA-cosB)^(2)+(sinA-sinB...

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

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KUMAR PRAKASHAN-TRIGONOMETRIC FUNCTIONS -PRACTICE WORK
  1. Prove that, (cos3A+2cos5A+cos7A)/(cosA+2cos3A+cos5A)=cos2A-sin2A.tan3A

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

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

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

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

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

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

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

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  9. Prove that, tan25^(@).tan15^(@)+tan15^(@)tan50^(@)+tan25^(@)tan50^(@)=...

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  10. Prove that, tan65^(@)=tan25^(@)+2tan40^(@).

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  11. If A+B+C=kpi, k inZ Then prove that, tanA+tanB+tanC=tanA.tanB.tanC

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  12. If A+B+C=kpi, k inZ Then prove that, cotB.cotC+cotC.cotA+cotA.cotB=1...

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  13. Prove that, sin5A=5cos^(4)AsinA-10cos^(2)Asin^(3)A+sin^(5)A

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  14. Prove that, sin^(3)A+sin^(3)((2pi)/(3)+A)+sin^(3)((4pi)/(3)+A)=-(3)/(4...

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  15. Prove that, cos5A=16cos^(5)A-20cos^(3)A+5cosA

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  16. Prove that, (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

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  17. Prove that, sin4A=4sinAcos^(3)A-4cosAsin^(3)A

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  18. If 2costheta=x+(1)/(x) then prove that, 2cos3theta=x^(3)+(1)/(x^(3)).

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  19. Find the general solutions of the following equations : 2sintheta+1=...

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  20. Find the general solutions of the following equations : cos3theta=-(...

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