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Prove: sqrt((1+sinA)/(1-sinA))=secA+tanA...

Prove: `sqrt((1+sinA)/(1-sinA))=secA+tanA`

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Prove that: i) sqrt((1-cosA)/(1+cosA))="cosec"A-cotA ii) sqrt((1+sinA)/(1-sinA))=secA-tanA

Prove the following identity, where the angles involved are acute angles for which the expressions are defined. sqrt((1+sinA)/(1-sinA))=secA+tanA

Prove that: sqrt((1-sinA)/(1+sinA))={(secA-tanA,if -pi/2 lt A lt pi/2),(tanA-secA ,if pi/2 lt A lt (3pi)/2):}

Prove: 1/(1+sinA)+1/(1-sinA)=2sec^2A

Prove that : sqrt((1+sinA)/(1-sinA))-sqrt((1-sinA)/(1+sinA))=2tanA

Prove the following identities : sqrt((1+sinA)/(1-sinA))=(cos A)/(1-sin A)

Prove: secA(1-sinA)(secA+tanA)=1

Prove: (secA-tanA)^2=(1-sinA)/(1+sinA)

Prove that : (i) (1)/(1-cosA)+(1)/(1+cosA)=2"cosec"^(2)A " " (ii) (1)/(1-sinA)-(1)/(1+sinA)=2secAtanA

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RD SHARMA ENGLISH-TRIGONOMETRIC IDENTITIES-All Questions
  1. Prove: (secA-tanA)/(secA+tanA)=(cos^2A)/((1+sinA)^2)

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  2. Prove: (1+cosA)/(sinA)=(sinA)/(1-cosA)

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  3. Prove: sqrt((1+sinA)/(1-sinA))=secA+tanA

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

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  5. Prove: (secA-tanA)^2=(1-sinA)/(1+sinA)

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  6. Prove: (1-cosA)/(1+cosA)=(cotA-cos e c\ A)^2

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

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

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

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  11. Prove : (tan^2A)/(1+tan^2A)+(cot^2A)/(1+cot^2A)=1

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

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  13. (1+costheta+sintheta)/(1+costheta-sintheta)=(1+sintheta)/(costheta)

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  14. Prove that: (sintheta-costheta+1)/(sintheta+costheta-1)=1/(sectheta-ta...

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

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

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

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

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

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

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