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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. : `(cosA)/(1+sinA)+(1+sinA)/(cosA)=2secA` .

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MBD-INTRODUCTION TO TRIGONOMETRY-EXERCISE
  1. Prove that (tantheta+sintheta)/(tantheta-sintheta)=(sectheta+1)/(secth...

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

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

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

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

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  6. Prove that (1-sintheta)/(1+sintheta)=(sectheta-tantheta)^2 .

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  7. Prove that (sintheta-2sin^3theta)/(2cos^3theta-costheta)=tantheta .

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  8. tantheta-cottheta=(2sin^2theta-1)/(sinthetacostheta)=(1-2cos^2theta)/(...

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

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  10. Prove that (1+tan^2theta)(1-sintheta)(1+sintheta)=1 .

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  11. Prove that (1 +cottheta-cosectheta)(1+tantheta+sectheta)=2.

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

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  13. Prove that sin^4theta+cos^4theta=1-2sin^2thetacos^2theta .

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

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

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  16. Prove that cottheta+tantheta=secthetacosectheta .

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

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

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

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

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