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Prove that: sin^(2)(pi/8+A/2)-sin^(2)(pi...

Prove that: `sin^(2)(pi/8+A/2)-sin^(2)(pi/8-A/2)=1/sqrt(2)sinA`

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Prove that: sin^(2)((pi)/(8)+(A)/(2))-sin^(2)((pi)/(8)-(A)/(2))=(1)/(sqrt(2))sin A

4.Prove that sin^(2)((pi)/(8))+sin^(2)((3 pi)/(8))=1

Prove that cos^(2)(pi/8-A/2)-cos^(2)(pi/8+A/2) [1-sin^(2)(pi/8-A/2)]-[1-sin^(2)(pi/8+A/2)] =sin^(2)(pi/8+A/2)-sin^(2)(pi/8-A/2) =sin{(pi/8+A/2)+(pi/8-A/2)} sin{(pi/8+A/2)-(pi/8-A/2)} s=sinpi/4. sinA=1/sqrt(2)sinA =RHS Hence Proved.

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

Prove that :cos((pi)/(12))-sin((pi)/(12))=(1)/(sqrt(2))

Prove that: sin^(4)((pi)/(8))+sin^(4)((3 pi)/(8))+sin^(4)((5 pi)/(8))+sin^(4)((7 pi)/(8))=(3)/(2)

Prove that: (sin^(2)pi)/(18)+(sin^(2)pi)/(9)+(sin^(2)(7 pi))/(18)+(sin^(2)(4 pi))/(9)=2

Prove that: sin ^ (2) ((pi) / (18)) + sin ^ (2) ((pi) / (9)) + sin ^ (2) ((7 pi) / (18)) + sin ^ (2) ((4 pi) / (9)) = 2

" 1.Prove that : "sin^(2)(pi)/(6)+cos^(2)(pi)/(3)-tan^(2)(pi)/(4)=-(1)/(2)

Prove that: i) sin^(-1)(1/sqrt(5))+sin^(-1)(2/sqrt(5))=pi/2

NAGEEN PRAKASHAN-TRIGNOMETRIC FUNCTIONS-EXERCISES 3D
  1. Prove that: cos(pi/4+A)+cos(pi/4-A)=sqrt(2)cosA

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  2. Prove that: cos((3pi)/(4)+A)-cos((3pi)/(4)-A)=-sqrt(2)sinA

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  3. Prove that: sin^(2)(pi/8+A/2)-sin^(2)(pi/8-A/2)=1/sqrt(2)sinA

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. If tanB=(nsinAcosA)/(1-nsin^(2)A), prove that: tan(A-B)=(1-n)tanA

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

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

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  20. If A+B=225^(@), prove that: (cotA)/(1+cotA) xx (cotB)/(1+cotB) = 1/2

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