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If sectheta=x+(1)/(4x),prove that secthe...

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

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NAGEEN PRAKASHAN ENGLISH-INTRODUCTION TO TRIGONOMETRY-Exercise 8 C
  1. (sinA+cosecA)^2+(cosA+secA)^2=7+tan^2A+cot^2A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. If x=cotA+cosA,y=cotA,prove that : ((x-y)/(x+y))^(2)+((x-y)/(2))^(2)=1

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  17. If (cosA)/(cosB)=p,(sinA)/(sinB)=q,then show that (p^(2)(1-q^(2)))/(p^...

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  18. If cotalpha+tanalpha=mand(1)/(cosalpha)-cosalpha=n, then show that m(...

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  19. If acos^3theta+3acosthetasin^2theta=m and asin^3theta+3acos^2thetasin...

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  20. If x=(2sintheta)/(1+costheta+sintheta),t h e n(1-costheta+sintheta)/(1...

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