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Prove the following identities: (cosA...

Prove the following identities: `(cosA)/(1-tanA)+(sinA)/(1-cotA)=cosA+sinA`

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RD SHARMA-TRIGONOMETRIC IDENTITIES-All Questions
  1. Prove: (1-cosA)/(1+cosA)=(cotA-cos e c\ A)^2

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  2. Prove: 1/(secA-1)+1/(secA+1)=2\ cos e c\ AcotA

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  3. Prove the following identities: (cosA)/(1-tanA)+(sinA)/(1-cotA)=cos...

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  4. Prove: (cos e c\ A)/(cos e c\ A-1)+(cos e c\ A)/(cos e c\ A+1)=2sec^2A

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  5. Prove: (1+tan^2A)+(1+1/(tan^2A))=1/(sin^2A-sin^4A)

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  6. (tan^2A)/(1+tan^2A)+(cot^2A)/(1+cot^2A)=1

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  7. Prove that (cotA-cosA)/(cotA+cosA)=(cosecA-1)/(cosecA+1)

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  8. (1+costheta+sintheta)/(1+costheta-sintheta)=(1+sintheta)/(costheta)

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

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

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

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

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

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

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

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

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

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

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

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

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