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Prove that : (sec^(2)A-1)("cosec"^(2)A-...

Prove that : `(sec^(2)A-1)("cosec"^(2)A-1)=1`

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NAGEEN PRAKASHAN ENGLISH-INTRODUCTION TO TRIGONOMETRY-Exercise 8 C
  1. Prove that tan^(2)theta+cot^(2)theta+2=sec^(2)theta cosec^(2)theta

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  2. Prove that (tanA+cotA)^(2)="cosec"^(2)A+sec^(2)A.

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  3. Prove that : (sec^(2)A-1)("cosec"^(2)A-1)=1

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  4. Prove the following identities: cosec^4A-sec^2A=tan^4A+tan^2A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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