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Prove the following : cos^6A-sin^6A = ...

Prove the following : `cos^6A-sin^6A`
= `cos2A(1-1/4 sin^2 2A)`

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MBD PUBLICATION-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. Prove the following : Express 4cosA.cosB.cosC as the sum of four cosin...

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  2. Express cos2A+cos2B+cos2C+cos2(A+B+C) as the product of three cosines.

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  3. Prove the following : cos^6A-sin^6A = cos2A(1-1/4 sin^2 2A)

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  4. Prove the following : cos^6A+sin^6A = 1/4 (1+3 cos^2 2A)

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  5. Prove the following : cos^3A.cos3A+sin^3Asin3A = cos^3 2A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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