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Prove that: cos((3pi)/(4)+A)-cos((3pi)...

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

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cos((3pi)/(4)+x)-cos((3pi)/(4)-x) = -sqrt(2)sinx

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Prove that: cos((3pi)/4+x)-cos((3pi)/4-x\ )=sqrt(2)sinx

Prove that: i) sin(5pi)/(18) - cos(4pi)/(9) = sqrt(3)sinpi/9 ii) cos(3pi)/4+A-cos((3pi)/(4)-A)=-sqrt(2)sinA

Prove that: cos(pi/4+A)+cos(pi/4-A)=sqrt(2)cosA

Prove that: cos(pi/7)cos((2pi)/7)cos((4pi)/7)=-1/8

Prove that : cos(pi/7)cos((2pi)/7) cos((3pi)/7)=1/8

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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