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Prove that : (1-tan^(2)theta)/(cot^(2)...

Prove that : `(1-tan^(2)theta)/(cot^(2)theta-1)=tan^(2)theta`

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(1-cot^(2)theta)/(tan^(2)theta-1)=cot^(2)theta

Prove that : (tan^(2)theta)/(1+tan^(2)theta)+(cot^(2)theta)/(1+cot^(2)theta)=1

Prove that 1/(1+tan^2 theta)+1/(1+cot^2 theta)=1

Prove that : (tan^(3) theta)/(1+tan^(2)theta) +(cot^(3)theta)/(1+cot^(2)theta) = sec theta "cosec " theta - 2 sin theta cos theta .

Prove that (tan^(2)2theta-tan^(2)theta)/(1-tan^(2)2thetatan^(2)theta)=tan 3 theta tan theta .

Prove that : (1 - tan^(2) theta)/(1 + tan^(2) theta) = cos^(2) theta - sin^(2) theta

Show that, (1+tan^2theta)/(1+cot^2 theta)=tan^2theta

Prove each of the following identities : (i) (1- tan^(2) theta)/(1+ tan^(2) theta) = ( cos^(2) theta - sin^(2) theta) (ii) (1- tan^(2) theta)/(cot^(2) -1) = tan^(2) theta

Prove: (1+tan^(2)theta)/(1+cot^(2)theta)=((1-tan theta)/(1-cot theta))^(2)=tan^(2)theta

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NAGEEN PRAKASHAN-INTRODUCTION TO TRIGONOMETRY-Exercise 8 C
  1. Prove the following identities: cosec^4A-sec^2A=tan^4A+tan^2A

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  2. Prove that : (i) tan^(2)A-sin^(2)A=tan^(2)A*sin^(2)A (i...

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  3. Prove that : (1-tan^(2)theta)/(cot^(2)theta-1)=tan^(2)theta

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  4. Prove that : (sectheta-tantheta)^(2)=(1-sintheta)/(1+sintheta)

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  5. Prove that : sec^(2)theta+"cosec"^(2)theta=sec^(2)theta*"cosec" ^(2)t...

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  6. Prove that : (sinA+cosA)^(2)+(sinA-cosA)^(2)=2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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