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Prove that: (cosA-cosB)^(2)+(sinA-sinB...

Prove that:
`(cosA-cosB)^(2)+(sinA-sinB)^(2)=4sin^(2)(A-B)/(2)`

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NAGEEN PRAKASHAN-TRIGNOMETRIC FUNCTIONS-EXERCISES 3E
  1. Express each of the following as a sum or difference of sine and cosin...

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  2. Evaluate: sin521/2^(@) cos71/2^(@)

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  3. Prove that: cos(45^(@)+A) cos(45^(2)-A)=1/2 cos2A

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  4. Prove that: cosA. Cos(60^(@)+A)cos(60^(2)-A)=1/4 cos3A

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  5. Prove that: sinA. Sin(60^(2)+A).sin(120^(@)+A)=1/4sin3A

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  6. Prove that: tan(pi/3-A).tan(pi/3+A)= (2cos2A+1)/(2cos2A-1)

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  7. Prove that: i) sin20^(@)sin40^(@)sin60^(@)sin80^(@)=3/16 ii) sin10...

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  8. Prove that: i) cos10^(@)cos30^(@)cos50^(@)cos70^(@)=3/16 ii) cos20...

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  9. Prove that tan20^0tan40^0tan80^0=tan60^0

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  10. Prove that: tan(A+B)/(2) + tan(A-B)/(2) = (2sinA)/(cosA+cosB)

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  11. Prove that: i) sin50^(@)-sin70^(@)+sin10^(@)=0 ii) sin(60^(@)+A)+s...

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  12. Prove that: i) sin(5pi)/(18) - cos(4pi)/(9) = sqrt(3)sinpi/9 ii) c...

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  13. Prove that: (sinA+sinB)/(sinA-sinB) = tan(A+B)/(2). Cot(A-B)/(2)

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  14. Prove that: (sin9A-sin7A)/(cos7A-cos9A) = cot8A

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  15. Prove that: (cos2A+cos3A+cos4A)/(sin2A+sin3A+sin4A)= cot3A

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  16. Prove that: (sin7A-2sin4A+sinA)/(cos7A-2cos4A+cosA)=tan4A

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

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  18. Prove that: (cosA-cosB)^(2)+(sinA-sinB)^(2)=4sin^(2)(A-B)/(2)

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  19. Prove that: cos2theta.costheta/2-cos3theta.cos(9theta)/(2)=sin5theta...

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