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Prove the following : (sintheta-costheta...

Prove the following : `(sintheta-costheta+1)/(sintheta+costheta-1)=(1)/(sectheta-tantheta)` .

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MBD-INTRODUCTION TO TRIGONOMETRY-EXERCISE
  1. Prove that sec A (1 -sin A) (sec A + tan A) =1.

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  2. Prove the following : (cot A - cos A)/(cot A + cos A)= (cosec A -1)/(c...

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  3. Prove the following : (sintheta-costheta+1)/(sintheta+costheta-1)=(1)/...

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  4. Prove the following : tan^2A-tan^2B=(sin^2A-sin^2B)/(cos^2Acos^2B) .

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  5. (sec A - cos A) (cot A + tan A) = tan A sec A.

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  6. sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A .

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  7. (cosec theta -sin theta) (sec theta - cos theta) (tan theta + cot thet...

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  8. (1 + cot A — cosec A) (1 + tan A + sec A) = 2 .

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  9. (sintheta+cosectheta)^2+(costheta+sectheta)^2=tan^2theta+cot^2+7 .

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  10. tan^2theta+cot^2theta+2=sec^2thetacoses^2theta .

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  11. Prove that cosA/(1-tanA)-(sin^2A)/(cosA-sinA)== sin A + cos A. .

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  12. (1+sintheta)/(1-sintheta)=1+(2tantheta)/costheta+2tan^2theta .

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

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  14. (1+costheta+sintheta)/(1+costheta-sintheta)=(1+sintheta)/costheta .

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

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

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

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

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  19. 2sec^2theta-sec^4theta-2cosec^2theta+cosec^4theta=cot^4theta-tan^4thet...

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

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