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Prove the following (1+tan^2theta) /(1+c...

Prove the following
`(1+tan^2theta) /(1+cot^2theta) =((1+tantheta) /(1+cottheta))^2 =tan^2theta`

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Prove the following (sec ^2theta -1) cos^2 theta=sin^2theta

Prove the following 1+(cot^2theta) /(1+cosectheta)=cosectheta

Prove the following 1/(1-sintheta) +1/(1+sintheta) =2sec^2theta

Prove the following costheta/(1-tantheta) +sintheta/(1-cottheta)=sintheta+costheta

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KALYANI PUBLICATION-RELATIONS BETWEEN TRIGONOMETRIC RATIOS AND RELATED IDENTITIES-EXERCISE
  1. Prove the following sqrt{(1-sintheta) /(1+sintheta)} =sectheta-tanthet...

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  2. Prove the following (cosectheta-sintheta)(sectheta-costheta)=1//(tanth...

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  3. Prove the following (1+tan^2theta) /(1+cot^2theta) =((1+tantheta) /(1+...

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  4. Prove the following sin^4theta-cos^4theta=sin^2theta-cos^2theta=1-2cos...

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  5. Prove the following sin^6theta+cos^6theta=1-3sin^2thetacos^2theta

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  6. Prove the following 2sec^2theta-2cosec^2theta-sec^4theta+cosec^4theta=...

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  7. Prove the following (cos^2theta) /(1-tantheta) +sin^3theta/(sintheta-c...

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  8. Prove the following (sintheta-2sin^3theta) /(2cos^3theta-costheta) =ta...

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  9. Prove the following (sintheta +cosectheta) ^2+(costheta+sectheta) ^2=7...

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  10. If (sec A + tan A)(sec B + tan B)(sec C + tan C) = (sec A- tan A)(sec ...

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  11. If sin^2theta + sin^ 4theta = 1, then prove that cos^2theta+ costheta...

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  12. If tan^4theta - tan^2 theta= 1, then prove that cos^4theta+ cos^2theta...

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  13. If 3 tantheta+ cottheta =5cosec theta, then prove that costheta=1/2

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  14. If 7 sin^2theta + 3 cos^2 theta= 4, then prove that tantheta = 1/s...

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  15. If cosectheta + cottheta= k, then prove that costheta=(k^2-1) /(k^2+1)

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  16. If tantheta+ cot theta = 2, then prove that tan^10theta + cot^10 theta...

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  17. If sintheta + cosectheta= 2, then prove that sin^100theta + cosec^100 ...

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  18. If sintheta - costheta = 1, then prove that sintheta + costheta =+-1

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  19. If cos^2theta- sin^2theta= tan^2 phi, then prove that cos^2phi – sin^2...

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  20. If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha)then prove that sqr...

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