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Prove the following : (1-tan^2(45^@-A))/...

Prove the following : `(1-tan^2(45^@-A))/(1+tan^2(45^@-A))` = sin2A

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L.H.S.
`(1-tan^2(45^@-A))/(1+tan^2(45^@-A)) = cos2(45^@-A)`
= cos(`90^@`-2A) = sin2A= R.H.S.
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MBD PUBLICATION-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. Prove the following : cos(A+B)+sin(A-B) 2sin(45^@+A)cos(45^@+B)

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  2. Prove the following : cos4A-cos4B = 8(cosA-cosB)(cosA+cosB)(cosA-sin...

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  3. Prove the following : (1-tan^2(45^@-A))/(1+tan^2(45^@-A)) = sin2A

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  4. Prove the following : (cosA+sinA)/(cosA-sinA)-(cosA-sinA)/(cosA+sinA) ...

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  5. Prove the following : (1-cos2A+sin2A)/(1+cos2A+sin2A) = tanA

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  6. Prove the following : (sin(A+B)+cos(A-B))/(sin(A-B)+cos(A+B)) = sec2...

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  7. Prove the following : (cos7alpha+cos3alpha-cos5alpha-cosalpha)/(sin7al...

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  8. Prove the following : (sintheta+sin3theta+sin5theta+sin7theta)/(costhe...

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  9. Prove the following : Express 4cosA.cosB.cosC as the sum of four cosin...

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

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

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

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

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

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

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

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

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

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

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

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