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Prove tantheta/(sectheta-1)+(tantheta)/(...

Prove `tantheta/(sectheta-1)+(tantheta)/(sectheta+1)=2cosectheta` .

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Prove that sqrt((sectheta-tantheta)/(sectheta+tantheta))=sectheta-tantheta .

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

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

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

Prove that cottheta+tantheta=secthetacosectheta .

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

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

Prove the following identities, where the angles involved are acute angles for which the expressions are defined. : (tantheta)/(1-cottheta)+(cottheta)/(1-tantheta)=1+secthetacosectheta .

If cottheta=3/4 prove that sqrt((sectheta-cosectheta)/(sectheta+cosectheta))=1/sqrt7 .

MBD-INTRODUCTION TO TRIGONOMETRY-EXERCISE
  1. Prove that cosA/(1-tanA)-(sin^2A)/(cosA-sinA)== sin A + cos A. .

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  2. (1+sintheta)/(1-sintheta)=1+(2tantheta)/costheta+2tan^2theta .

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  3. Prove tantheta/(sectheta-1)+(tantheta)/(sectheta+1)=2cosectheta .

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  4. (1+costheta+sintheta)/(1+costheta-sintheta)=(1+sintheta)/costheta .

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  5. Prove the following identities, where the angles involved are acute an...

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  6. tantheta/(1-cottheta)+cottheta/(1-tantheta)=1+tantheta+cottheta .

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  7. (sinA+cosA)/(sinA-cosA)+(sinA-cosA)/(sinA+cosA)=2/(sin^2A-cos^2A)=2/(1...

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  8. (tan^3theta)/(1+tan^2theta)+(cot^3theta)/(1+cot^2theta)=secthetacosect...

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  9. 2sec^2theta-sec^4theta-2cosec^2theta+cosec^4theta=cot^4theta-tan^4thet...

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

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  11. (tanA+secA-1)/(tanA-secA+1)=(1+sinA)/cosA .

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  12. 1/(cosectheta+cottheta)-1/sintheta=1/sintheta-1/(cosectheta-cottheta) ...

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  13. tantheta/(1-cottheta)+cottheta/(1-tantheta)=1+tantheta+cottheta .

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  14. (cosecA)/(cosecA-1)+(cosecA)/(cosecA+1)=2+2tan^2A .

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  15. (tanA-tanB)^2+(1+tanAtanB)^2=sec^2Asec^2B .

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  16. If cosalpha/cosbeta=m and cosalpha/sinbeta=n then Show that (m^2+n^2) ...

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  17. If costheta+sintheta=sqrt2costheta ,then show that costheta-sintheta=...

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  18. If tantheta+sintheta=m,tantheta-sintheta=n , then show that m^2-n^2=4s...

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  19. If sectheta= x+1/(4x) , then prove that sectheta+tantheta=2x or 1/(2x)...

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  20. IF sintheta+sin^2theta=1 prove that cos^2theta+cos^4theta=1 .

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