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

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

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L.H.S. = `(1-cos2A+sin2A)/(1+cos2A+sin2A)`
`(2sin^2A+2sinAcosA)/(2cos^2A+2sinAcosA)`
`(2sinA(sinA+cosA))/(2cosA(cosA+sinA))`
tanA = R.H.S.
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MBD PUBLICATION-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. Prove the following : (1-tan^2(45^@-A))/(1+tan^2(45^@-A)) = sin2A

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

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

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

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

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

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

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

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

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

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

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

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

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