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Prove that : (i) (1-cosA)/(sinA)=(s...

Prove that : (i) `(1-cosA)/(sinA)=(sinA)/(1+cosA)`
(ii) ` (costheta)/(1-sintheta)=(1+sintheta)/(costheta)`

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NAGEEN PRAKASHAN ENGLISH-INTRODUCTION TO TRIGONOMETRY-Exercise 8 C
  1. Prove that : (sinA+cosA)^(2)+(sinA-cosA)^(2)=2

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  2. Prove that : sin^(4)theta-cos^(4)theta=2sin^(2)theta-1

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  3. Prove that : (i) (1-cosA)/(sinA)=(sinA)/(1+cosA) (ii) ...

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  4. Prove that : (1+sintheta)/(costheta)+(costheta)/(1+sintheta)=2secthe...

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  5. Prove that : (1-costheta)/(sintheta)+(sintheta)/(1-costheta)=2"cosec...

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  6. Prove that : (i) (1)/(1-cosA)+(1)/(1+cosA)=2"cosec"^(2)A " " (...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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