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Prove that (costheta-sintheta+1)/(costhe...

Prove that `(costheta-sintheta+1)/(costheta+sintheta-1)=c o s e ctheta+cottheta`

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RD SHARMA-TRIGONOMETRIC IDENTITIES-All Questions
  1. (1+costheta+sintheta)/(1+costheta-sintheta)=(1+sintheta)/(costheta)

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

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  3. Prove that (costheta-sintheta+1)/(costheta+sintheta-1)=c o s e ctheta+...

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  4. Prove: tan^2A+cot^2A=sec^2A cos e c^2A-2

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  5. Prove: (1-tan^2A)/(cot^2A-1)=tan^2A

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  6. Prove: 1+(cot^2theta)/(1+cos e c\ theta)=cos e c\ theta

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  7. Prove: (costheta)/(cos e c\ theta+1)+(costheta)/(cos e c\ theta-1)=2ta...

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

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  9. Prove: (tan^3theta)/(1+tan^2theta)+(cot^3theta)/(1+cot^2theta)=secthet...

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  10. Prove: (tantheta+1/(costheta))^2+(tantheta-1/(costheta))^2=2((1+sin^2t...

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  11. Prove the following identity: (1/(sec^2theta-cos^2theta)+1/(cos e c^2t...

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  12. Prove: ((1+sintheta-costheta)/(1+sintheta+costheta))^2=(1-costheta)/(1...

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  13. Prove: (secA+tanA-1)(secA-tanA+1)=2tanA

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  14. Prove: (1+cotA-cos e c\ A)(1+tanA+secA)=2

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  15. Prove: (cos e c\ theta-sectheta)(cottheta-tantheta)=(cos e c\ theta+se...

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  16. Prove: (secA-cos e c\ A)(1+tanA+cotA)=tanAsecA-cotA cos e c\ A .

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  17. (cosAcosecA-sinAsecA)/(cosA+sinA)=cosecA-secA

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  18. Prove: (sinA)/(secA+tanA-1)+(cosA)/(cos e c\ A+cotA-1)=1

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  19. Prove: (tanA)/((1+tan^2A)^2)+(cotA)/((1+cot^2A)^2)=sinAcosA

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  20. Prove: sec^4A(1-sin^4A)-2tan^2A=1

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