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Prove the following identities: cosec...

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

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Prove the following identities: sec^(4)A-sec^(2)A=tan^(4)A+tan^(2)A

sec^(4)A-sec^(2)A=tan^(4)A+tan^(2)A

Prove the following identity: sec^(4)theta-sec^(2)theta=tan^(4)theta+tan^(2)theta

Prove the following identity: (sec A sec B+tan A tan B)^(2)-(sec A tan B+tan A sec B)^(2)=1

Prove the following identities: 2sec^(2)theta-sec^(4)theta-2cos ec^(2)theta+cos ec^(4)theta=cot^(4)theta-tan^(4)theta

Prove the following identities: 2sec^(2)theta-sec^(4)theta-2cos ec^(2)theta=cot^(4)theta-tan^(4)theta

Prove the following identities: (sec-tan theta)/(sec theta+tan theta)=1-2sec theta tan theta+2tan^(2)theta

Prove the following identities: (1+tan A tan B)^(2)+(tan A-tan B)^(2)=sec^(2)A sec^(2)B(tan A+csc B)^(2)-(cot B-sec A)^(2)=2tan A cot B(csc A+sec B)

Prove the following identities: (sin A+sec A)^(2)+(cos A+csc A)^(2)=(1+sec A csc A)^(2)cot^(2)A((sec A-1)/(1+sin A))+sec^(2)A((sin A-1)/(1+sec A))=0

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

NAGEEN PRAKASHAN-INTRODUCTION TO TRIGONOMETRY-Exercise 8 C
  1. Prove that : (tanA+cotA)^(2)=sec^(2)A+"cosec"^(2)A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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