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Prove the following identity : 2 sec^2...

Prove the following identity :
`2 sec^2 theta- sec^4 theta-2 cosec^2 theta+ cosec^4 theta= cot^4 theta-tan^4 theta`.

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2sec^2theta-sec^4theta-2cosec^2theta+cosec^4theta=cot^4theta-tan^4theta .

Prove the following identity : cosec^6 theta- cot^6 theta =3 cot^2 theta cosec^2 theta+1 .

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Prove the following identity : sin theta cot theta+ sin theta cosec theta=1 + cos theta .

Prove the following identity : sin^4 theta+ cos^4 theta= 1-2 sin^2 theta cos^2 theta .

Prove the following identity : 2 (sin^6 theta+ cos^6 theta)-3 (sin^4 theta+ cos^4 theta)+1=0 .

Prove the following identity : cos^4 theta- sin^4 theta= cos^2 theta-sin^2 theta= 2 cos^2 theta-1=1-2 sin^2 theta .

Prove the following identity : (sin theta+ cos theta) (sec theta+ cosec theta) =2+ sec theta cosec theta .

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove the following identity : sec^6 theta- tan^6 theta=1+3 tan^2 th...

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  2. Prove the following identity : cosec^6 theta- cot^6 theta =3 cot^2 t...

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  3. Prove the following identity : 2 sec^2 theta- sec^4 theta-2 cosec^2 ...

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  4. Prove the following identity : (sin theta)/(1+cos theta)+ (tan theta...

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  5. Prove the following identity : (sin theta)/(1+cos theta)+ (sin theta...

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  6. Prove the following identity : (tan theta-cot theta)/ (sin theta cos...

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  7. Prove the following identity : (cosec theta)/(cot theta+tan theta)= ...

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  8. Prove the following identity : (1-cos theta)/(sin theta)= (sin theta...

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  9. Prove the following identity : (sin theta)/(1-cos theta)= (1+cos the...

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  10. Prove the following identity : (cot^2 theta)/((1- cosec theta)^2)= (...

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  11. Prove the following identity : cot^2 theta ((sec theta-1)/(1+sin the...

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  12. Prove the following identity : (tan theta)/(1-cot theta)+ (cot theta...

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  13. (1 + cot A — cosec A) (1 + tan A + sec A) = 2 .

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  14. Prove the following identities, where the angles involved are acute an...

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  15. Prove the following identity : (1 - tan x)^2+(1 -cot x)^2 = (sec x -...

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  16. Prove the following identity : (sec theta-cos theta) (cosec theta-si...

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  17. Prove the following identity : (sin theta+ sec theta)^2 +(cos theta+...

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  18. Prove the following identity : sqrt (sec^2 theta+ cosec^2 theta)= ta...

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  19. Prove the following identity : 1/(cosec theta- cot theta)-1/(sin the...

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  20. Prove the following identity : 1/(sec theta+tan theta) -1/(cos theta...

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