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Prove that: sin^(2)A+sin^(2)(60^(@)+A)...

Prove that:
`sin^(2)A+sin^(2)(60^(@)+A)+sin^(2)(A-60^(@))=3/2`

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NAGEEN PRAKASHAN-TRIGNOMETRIC FUNCTIONS-EXERCISES 3F
  1. prove that (sin2A)/(1-cos2A)=cotA

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  2. Prove that: (cos2A)/(1+sin2A) = tan(pi/4-A)

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  3. Prove that: tan(pi/4+A)+tan(pi/4-A) = 2sec2A

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  4. Statement I : sin^2pi/8+sin^2(3pi)/8+sin^2(5pi)/8+sin^2(7pi)/8=2 State...

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  5. Prove that: sin^(2)A+sin^(2)(60^(@)+A)+sin^(2)(A-60^(@))=3/2

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  6. i) Prove that: (1-sin2A)/(1+sin2A) = tan^(2)(pi/4-A) ii) If costheta...

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  7. Prove that: sqrt(3)"cosec"20^(@)-sec20^(@)=4

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  8. Evaluate the following: i) sin\ pi/12 ii) sin\ pi/8, iii) cos\ pi/...

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  9. Prove that: "cot"pi/(24)=sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6)

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  10. If sinA = -5/13 and pi lt lt (3pi)/(2), find the values of the followi...

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  11. If tanA=-3/4 and pi/2 lt A lt pi, find the values of the following: ...

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  12. Prove that: (1+sinA-cosA)/(1+sinA+cosA) = tanA/2

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  13. Prove that: tanA/2+ cotA/2=2 "cosec"A

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  14. Prove that: s in^4pi/8+s in^4(3pi)/8+s in^4(5pi)/8+s in^4(7pi)/8=3/2

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  15. Prove that: 1+cos^2 2theta=2(cos^4theta+sin^4theta)

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  16. Prove that: tanA(1+sec2A)=tan2A

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  17. Prove that: sqrt(2+sqrt(2+sqrt(2+2cos8A)))=2cosA

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  18. Prove that: cos6A=32cos^(6)A-48cos^(4)A+18cos^(2)A-1

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

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  20. Prove that: cos^(3)A + cos^(3)((2pi)/(3)+A) + cos^(3)((4pi)/3+A) = 3/...

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