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Prove: sec^6theta=tan^6theta+3tan^2theta...

Prove: `sec^6theta=tan^6theta+3tan^2thetasec^2theta+1`

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RD SHARMA ENGLISH-TRIGONOMETRIC IDENTITIES-All Questions
  1. Prove: (1+tan^2theta)/(1+cot^2theta)=((1-tantheta)/(1-cottheta))^2=tan...

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  2. Prove: (1+sectheta)/(sectheta)=(sin^2theta)/(1-costheta)

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  3. Prove: sec^6theta=tan^6theta+3tan^2thetasec^2theta+1

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  4. Prove: cos e c^6theta=cot^6theta+3cot^2thetacos e c^2theta+1

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  5. Prove that:((1+tan^2theta)cottheta)/(c o s e c^2theta)=tantheta

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  6. Prove: (1+cosA)/(sin^2A)=1/(1-cosA)

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  7. Prove: (secA-tanA)/(secA+tanA)=(cos^2A)/((1+sinA)^2)

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

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

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

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

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

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

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

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

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

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

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  19. (1+costheta+sintheta)/(1+costheta-sintheta)=(1+sintheta)/(costheta)

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

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