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Prove that: cos^(2)((pi)/(8)) + cos^(2...

Prove that:
`cos^(2)((pi)/(8)) + cos^(2)((3pi)/(8)) + cos^(2)((5pi)/(8))+ cos^(2)((7pi)/(8))=2`

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NAGEEN PRAKASHAN ENGLISH-TRIGNOMETRIC FUNCTIONS-EXERCISES 3D
  1. Prove that: sin^2(pi/8+A/2)-sin^2(pi/8-A/2)=1/sqrt(2)sinA

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  2. Prove that: cos^2pi/8+sin^2(3pi)/8+sin^2(5pi)/8sin^2(7pi)/8=2

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  3. Prove that: cos^(2)((pi)/(8)) + cos^(2)((3pi)/(8)) + cos^(2)((5pi)/(...

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  4. Prove that: i) tan36^(@)+tan9^(@)+tan36^(@)tan9^(@)=1

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  5. Prove that: (cos8^(@)-sin8^(@))/(cos8^(@)+sin8^(@))=cot53^(@)

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  6. If A-B=pi/4, then prove that: (1+tanA)(1-tanB)=2

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  7. Prove that: (cos(60^(@)-A)+sin(30^(@)-A))/(cos(30^(@)-A)-sin(60^(@)-A)...

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  8. i) If A+B=pi/4 prove that: (cotA-1)(cotB-1)=2

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  9. Prove that: (tan(pi/4+A)+tan(pi/4-A))/(tan(pi/4+A)-tan(pi/4-A))="cos...

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  10. Prove that: (sin(A-B))/(cosAcosB)+(sin(B-C))/(cosBcosc)+(sin(C-A))/(...

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  11. Prove that: sinAsin(B-C)+sinBsin(C-A)+sinCsin(A-B)=0

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  12. Prove that: cot2Acot3A-cot3Acot5A-cot5Acot2A=1

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  13. Prove that: cotA-cot2A="cosec"2A

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  14. Prove that: cos^2A+cos^2B-2cosA\ cos B cos\ (A+B)=sin^2(A+B)

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  15. If tan B=(n sin A cos A)/(1-n cos^(2)A), then tan(A+B) equals to

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  16. If tan B=(n sin A cos A)/(1-n cos^(2)A), then tan(A+B) equals to

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  17. If 2tanB +cotB=tanA, prove that: 2tan(A-B)=cotB

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  18. i) If tan (A+B) = n tan (A-B), prove that: (n+1)/(n-1) = (sin2A)/(sin...

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  19. If A+B=225^(@), then find the value of (cotA)/(1+cotA)xx(cot B)/(1+cot...

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  20. If cos(A+B)sin(C-D)="cos"(A-B)"sin"(C+D) , then write the value of t a...

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