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Prove that : (i) (1)/(1+tan^(2)thet...

Prove that :
(i) `(1)/(1+tan^(2)theta)+(1)/(1+cot^(2)theta)=1`
(ii) `sin^(2)theta+(1)/(1+tan^(2)theta)=1`

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(1+(1)/(tan^(2)theta))(1+(1)/(cot^(2)theta))=(1)/(sin^(2)theta-sin^(4)theta)

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

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

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NAGEEN PRAKASHAN-INTRODUCTION TO TRIGONOMETRY-Exercise 8 C
  1. Prove that : (i) (1)/(1+tan^(2)theta)+(1)/(1+cot^(2)theta)=1 ...

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  2. If costheta=(15)/(17), then find the value of sintheta.

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  3. Prove that : (i) 1+(cos^(2)theta)/(sin^(2)theta)-"cosec"^(2)theta=0...

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  4. Prove that 1+tan^2A/(1+secA)=secA

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  5. Prove that : (cotA-1)/(2-sec^(2)A)=(cotA)/(1+tanA)

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  6. tan^(2)theta+cot^(2)theta+2=sec^(2)theta cosec^(2)theta

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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