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

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

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Prove the following identity, where the angles involved are acute angles for which the expressions are defined. (viii) (sinA+cose c A)^2+(cosA+secA)^2=7+tan^2A+cot^2A

(sinA+cosA)^2+(sinA-cosA)^2=

Prove the following identities: (cosA)/(1-sinA)+(sinA)/(1-cosA)+1 = (sinAcosA)/((1-sinA)(1-cosA) ((1+cotA+tanA)(sinA-cosA)/(sec^3A-cos e c^3A)=sin^2Acos^2A

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

Prove that (sinA+cosA)^3 = 3(sinA+cosA) - 2 (sin^3A+cos^3A)

Prove the following identities: (sinA+cosA)/(sinA-cosA)+(sinA-cosA)/(sinA+cosA)=2/(sin^2A-cos^2A)=2/(2sin^2A-1)=2/(1-2cos^2A)

Prove that (1+sinA-cosA)^2+(1-sinA+cosA)^2=4(1-sinA.cosA)

Prove that: (1+sinA-cosA)/(1+sinA+cosA) = tan(A/2)

Prove that: cotA/2-tanA/2=(cosA/2)/(sinA/2)-(sinA/2)/(cosA/2) =(cos^(2)A/2-sin^(2)A/2)/(sinA/2cosA/2) =cosA/(1/2.(2sinA/2cosA/2)) =(2cosA)/(sinA)=2cotA = RHS. Hence Proved.

Prove that: (1+sinA-cosA)/(1+sinA+cosA)=tan(A/2)

NAGEEN PRAKASHAN ENGLISH-INTRODUCTION TO TRIGONOMETRY-Exercise 8 C
  1. If tanA+sinA=m and tanA-sinA=n, then prove that m^(2)-n^(2)=4sqrt(mn)...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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