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Prove that : sin^(6)A+cos^(6)A+3sin^(2...

Prove that : `sin^(6)A+cos^(6)A+3sin^(2)Acos^(2)A=1`

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NAGEEN PRAKASHAN ENGLISH-INTRODUCTION TO TRIGONOMETRY-Exercise 8 C
  1. Prove that : (i) (1)/(1-cosA)+(1)/(1+cosA)=2"cosec"^(2)A " " (...

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  2. Prove that : (i) (1)/(sectheta-tantheta)+(1)/(sectheta+tantheta)=2se...

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  3. Prove that : sin^(6)A+cos^(6)A+3sin^(2)Acos^(2)A=1

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  4. Prove that : (1+cottheta+"cosec"theta)(1+cottheta-"cosec"theta)=2cott...

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  5. Prove that : (secA+1)/(tanA)=(tanA)/(secA-1)

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  6. Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ

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  7. Prove that : (sinA-cosA)(cotA +tanA)=secA-"cosec"A

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  8. If sec θ + tan θ = 7, then evaluate sec θ – tan θ

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  9. Prove that : (tanA)/(1-cotA)+(cotA)/(1-tanA)=1+secA" cosec"A

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  10. (tanA+secA-1)/(tanA-secA+1)=(1+sinA)/(cosA)

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  11. If tanA+sinA=m and tanA-sinA=n, then prove that m^(2)-n^(2)=4sqrt(mn)...

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  12. If x=acostheta-bsinthetaandy=asintheta+bcostheta, then show that : ...

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  13. (sinA+cosecA)^2+(cosA+secA)^2=7+tan^2A+cot^2A

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  14. Prove that : (1-tanA)^(2)+(1-cotA)^(2)=(secA-"cosec"A)^(2)

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  15. Prove that : (secA-tanA)/(secA+tanA)=1-2secAtanA+2tan^(2)A

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  16. Prove that : sqrt((1+cosA)/(1-cosA))+sqrt((1-cosA)/(1+cosA))=2" cose...

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  17. If (1-sinA)(1-sinB)(1-sinC)=(1+sinA)(1+sinB)(1+sinC), then show that ...

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  18. If tan^2 theta= 1-e^2 prove that sec theta + tan^3 theta cosec theta=...

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  19. Prove that (sintheta-costheta+1)/(sintheta+costheta-1)=1/(sectheta-tan...

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  20. If (cosalpha)/(sinbeta)=n and (cosalpha)/(cosbeta)=m, then find cos^(2...

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