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(tanA+secA-1)/(tanA-secA+1)=(1+sinA)/(co...

`(tanA+secA-1)/(tanA-secA+1)=(1+sinA)/(cosA)`

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Prove the following identity, where the angles involved are acute angles for which the expressions are defined. (iv) (1+secA)/(secA)=(sin^2A)/(1-cosA)

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

Prove that: (1+cosA+sinA)/(1+cosA-sinA)=(1+sinA)/(cosA)

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

Prove that (tanA)/(1+secA) - (tanA)/(1-secA) = 2cosecA

Prove that: " "( tan A + sinA)/(tanA - sinA) = (sec A +1)/(secA -1)

Prove the following identities: (sinA+secA)^2+(cos"A"+"c o s e cA")^2=(1+secAcos e cA)^2 cot^2A((secA-1)/(1+sinA))+sec^2A((sinA-1)/(1+secA))=0

NAGEEN PRAKASHAN ENGLISH-INTRODUCTION TO TRIGONOMETRY-Exercise 8 C
  1. If sec θ + tan θ = 7, then evaluate sec θ – tan θ

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

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

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

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

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

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

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

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

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

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

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

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

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  14. If sectheta=x+(1)/(4x),prove that sectheta+tantheta=2xor(1)/(2x)*

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  15. If x=asecthetacosphi ,y=secthetasinphiandz=ctantheta,show that(x^(2))/...

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

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  17. Prove that : (sintheta-2sin^(3)theta)/(2cos^(3)theta-costheta)-tanth...

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  18. Eliminate alpha from x=asinalpha+bcosalphaandy=acosalpha-bsinalpha.

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  19. If 7("cosec "theta-1)=3cottheta,then prove that : 3("cosec " theta+1)=...

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  20. If x=(1+sintheta)/(costheta), prove that : sintheta=(x^(2)-1)/(x^(2)+...

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