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Prove the following identities, where th...

Prove the following identities, where the angles involved are acute angles for which the expressions are defined. : `(cosectheta-cottheta)^2=(1-costheta)/(1+costheta)` .

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MBD-INTRODUCTION TO TRIGONOMETRY-EXERCISE
  1. Prove tantheta/(sectheta-1)+(tantheta)/(sectheta+1)=2cosectheta .

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

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

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

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

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

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  7. 2sec^2theta-sec^4theta-2cosec^2theta+cosec^4theta=cot^4theta-tan^4thet...

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

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

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  10. 1/(cosectheta+cottheta)-1/sintheta=1/sintheta-1/(cosectheta-cottheta) ...

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

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

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

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

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

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

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

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

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  19. Evaluate without using trigonometric tables : cotthetatan(90^@-theta)-...

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  20. Prove that : (1+costheta-sin^2 theta)/(sintheta(1+costheta))=cottheta ...

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