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Prove the following : cot3A = (cot^3A-3c...

Prove the following : `cot3A = (cot^3A-3cotA)/(3cot^2A-1)`

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MBD PUBLICATION-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. Prove the following : cos^3A.cos3A+sin^3Asin3A = cos^3 2A

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  2. Prove the following : sin^4theta=3/8-1/2 cos2theta+1/8 cos4theta

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  3. Prove the following : cot3A = (cot^3A-3cotA)/(3cot^2A-1)

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  4. Prove the following : tan4theta = (4tantheta-4tan^3theta)/(1-6tan^2the...

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  5. Prove the following : 1/(tan3A-tanA)-1/(cot3A-cotA) = cot2A

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  6. Prove the following : cotA/(cotA-cot3A)-tanA/(tan3A-tanA) =1

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  7. Find the value of sin3^@, cos3^@

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  8. If sinA+sinB=a and cosA+cosB=b, show that tan(A+B) = (2ab)/(b^2-a^2)

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  9. If sinA+sinB=a and cosA+cosB=b, show that sin(A+B) = (2ab)/(b^2+a^2)

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  10. If sinA+sinB=a and cosA+cosB=b, show that cos(A+B) = (b^2-a^2)/(b^2+...

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  11. Prove the following : (1+sinA-cosA)/(1+sinA+cosA) = tan A//2

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  12. Prove the following : 8sin^4(1/2theta)-8sin^2(1/2theta)+1=cos2theta

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  13. Prove the following : cos^4(pi/8)+cos^4((3pi)/8)+cos^4((5pi)/8)+cos^4(...

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  14. Prove the following : cos^2(alpha/2)(1-2cosalpha)^2+sin^2(alpha/2)(1+2...

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  15. Prove the following : sin20^@.sin40^@.sin60^@.sin80^@ = 3/16

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  16. Prove the following : cos36^@.cos72^@.cos108^@.cos144^@ = 1/16

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  17. Prove the following : cos10^@.cos30^@.cos50^@.cos70^@ = 3/16

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  18. Prove the following : cos20^@.cos40^@.cos60^@.cos80^@ = 1/16

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  19. Prove the following : tan6^@.tan42^@.tan66^@.tan78^@ = 1

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  20. Prove the following : cot7(1/2)^@=sqrt6+sqrt3+sqrt2+2

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