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Prove that sintheta(cosectheta-sintheta)...

Prove that `sintheta(cosectheta-sintheta)=cos^2theta` .

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Prove that sin^4theta-cos^4theta=sin^2theta-cos^2theta .

Prove that sintheta/(1+costheta)+sintheta/(1-costheta)=2/sintheta .

Prove that sintheta/(1-costheta)=cosectheta+cottheta .

Prove that sin^3theta+cos^3theta=(sintheta+costheta)(1-sinthetacostheta) .

Prove that (sectheta+tantheta)(1-sintheta)=costheta .

Prove that (sintheta)/(cottheta+cosectheta)=2+sintheta/(cottheta-cosectheta) .

Prove that (cosectheta+cottheta)(1-costheta)=sintheta .

Prove that 1/(1+sintheta)+1/(1-sintheta)=2sec^2theta .

Prove that (sintheta)/(1+costheta)+(1+costheta)/sintheta=2cosectheta .

Prove that ((1+sintheta)^2+(1-sintheta)^2)/(2cos^2theta)=(1+sin^2theta)/(1-sin^2theta) .

MBD-INTRODUCTION TO TRIGONOMETRY-EXERCISE
  1. Prove that sin^4theta+cos^4theta=1-2sin^2thetacos^2theta .

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  2. Prove that sin^4theta-cos^4theta=sin^2theta-cos^2theta .

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  3. Prove that sintheta(cosectheta-sintheta)=cos^2theta .

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  4. Prove that cottheta+tantheta=secthetacosectheta .

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  5. Prove that (cosA+sinA)^2+(cosA-sinA)^2=2 .

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  6. Prove that tan^2theta-sin^2theta=tan^2thetasin^2theta .

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  7. Prove that sec^4theta-sec^2theta=tan^4theta+tan^2theta .

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  8. Prove that (1+tan^2theta)sinthetacostheta=tantheta .

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  9. Prove that (sectheta+tantheta)(1-sintheta)=costheta .

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  10. Prove that (cosectheta+cottheta)(1-costheta)=sintheta .

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  11. Prove that sin^3theta+cos^3theta=(sintheta+costheta)(1-sinthetacosthet...

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  12. Prove that sin^6theta+cos^6theta=1-3sin^2thetacos^2theta .

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  13. Prove that 1/(cosecA+cotA)=(cosecA-cotA) .

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  14. Prove that (cosecA+cotA)/(cosecA-cotA)=(cosecA+cotA)^2 .

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  15. Prove that (cosecA)/(cosecA-1)+(cosecA)/(cosecA+1)=2sec^2A .

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  16. Prove that (sec^2theta-sin^2theta)/tan^2theta=cosec^2theta-cos^2theta ...

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  17. Prove that:(1+cos^2A)/(sin^2A)=2cosec^2A-1

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  18. Prove that (1/costheta-costheta)(1/sintheta-sintheta)=1/(tantheta+cott...

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  19. Prove that (1-costheta)/(1+costheta)=(cosectheta-cottheta)^2 .

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  20. sqrt(sec^2theta+cosec^2theta)=tantheta+cottheta=sectheta.cosectheta. .

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