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Evaluate sin2A, cos2A and tan2A if: i)...

Evaluate `sin2A, cos2A` and `tan2A` if:
i) `sinA=5/13`, ii) `cosA=8/17`, iii) `tanA=4/3`

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To evaluate \( \sin 2A \), \( \cos 2A \), and \( \tan 2A \) for the given values of \( \sin A \), \( \cos A \), and \( \tan A \), we will follow a systematic approach. ### i) Given \( \sin A = \frac{5}{13} \) 1. **Find \( \cos A \)**: \[ \cos^2 A + \sin^2 A = 1 \] ...
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NAGEEN PRAKASHAN ENGLISH-TRIGNOMETRIC FUNCTIONS-EXERCISES 3F
  1. Evaluate sin2A, cos2A and tan2A if: i) sinA=5/13, ii) cosA=8/17, iii...

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  2. If cosA=-3/5 and pi/2 lt A lt pi, find the values of the following: ...

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  3. If tanA = 12/5 and pi lt A lt (3pi)/(2), find the values of the follow...

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  4. If tanA=1/7a n d tanB=1/3 , show that cos2A=sin4Bdot

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  5. prove that (sin2A)/(1-cos2A)=cotA

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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