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i) Prove that: (1-sin2A)/(1+sin2A) = tan...

i) Prove that: `(1-sin2A)/(1+sin2A) = tan^(2)(pi/4-A)`
ii) If `costheta=1/2(x+1/x)`, then prove that:
`cos2theta=1/2(x^(2)+1/x^(2))` and `cos3theta=1/2(x^(3)+1/x^(3))`

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NAGEEN PRAKASHAN ENGLISH-TRIGNOMETRIC FUNCTIONS-EXERCISES 3F
  1. Prove that: tan(pi/4+A)+tan(pi/4-A) = 2sec2A

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

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

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

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

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  6. Prove that: (1+cos. (pi)/8)(1+cos. (3pi)/8)(1+cos. (5pi)/8)(1+cos. (7...

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

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

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

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

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  11. Prove that: (1+sinA-cosA)/(1+sinA+cosA) = tan(A/2)

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  12. Prove that: tan(A/2)+ cot(A/2)=2 "cosec"A

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

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  15. i) Prove that: cos^(3)2A+3cos2A = 4(cos^(6)A-sin^(6)A) ii) Prove t...

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

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  17. Show that: sqrt(2+sqrt(2+sqrt(2+2cos8theta)))=2costheta,0<theta<pi/8

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  18. about to only mathematics

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

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  20. Prove that cos^(3)x+cos^(3)((2pi)/3+x)+cos^(3)((2pi)/3-x)=3/4 cos 3x

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