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(cosec theta -sin theta) (sec theta - co...

(cosec `theta` -sin `theta`) (sec `theta` - cos `theta`) (tan `theta` + cot `theta`) = 1.

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Prove the following identity : (sec theta-cos theta) (cosec theta-sin theta)=1/(tan theta+ cot theta) .

If A = [(cos theta, sin theta),(-sin theta, cos theta)] and B = [(sin theta, - cos theta), (cos theta, sin theta)] , evaluate A cos theta + B sin theta .

Prove that : (sec theta-tan theta)/(sec theta+tan theta)= 1-2 sec theta tan theta+ 2 tan^2 theta .

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

Prove that (1 +cot theta -cosec theta )(1+tan theta +sec theta )=2.

Prove that : (sin theta)/(1+cos theta) + (1+cos theta)/(sin theta)= 2 cosec theta .

Verify that [(cos theta, sin theta),(-sin theta, cos theta)] and [(cos theta, - sin theta),(sin theta, cos theta)] are inverse of each other.

Prove the following identity : (sin theta+ sec theta)^2 +(cos theta+ cosec theta)^2= (1+ sec theta cosec theta)^2 .

Let A = [ (cos theta, sin theta),(- sin theta, cos theta)] , then show that A ^(2) = [(cos 2 theta, sin 2 theta),( - sin 2 theta, cos 2 theta)]

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove the following identity : sin theta (1+tan theta)+ cos theta(1+...

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

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  3. (cosec theta -sin theta) (sec theta - cos theta) (tan theta + cot thet...

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  4. Prove the following identity : sin^2 A cos^2 B + cos^2 A sin^2 B + c...

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

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  6. Prove the following identity : (1+cos theta)/(1-cos theta)= (tan^2 t...

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  7. Prove the following identity : (1-sin theta)/(1+sin theta)= (sec the...

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

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

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  10. Prove the following identity : sqrt ((1+sin theta)/ (1-sin theta)) =...

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  11. Prove the following identity : cot^2 theta- cos^2 theta= cot^2 theta...

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

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

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  14. Prove the following identity : sec^4 theta- tan^4 theta =1+2 tan^2 t...

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  15. Prove the following identity : sin^6 theta+ cos^6 theta= 1-3 sin^2 t...

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

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  17. Prove the following identity : 2u6-3u4+1=0, where un =cos^n theta+ s...

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  18. Prove the following identity : sec^6 theta- tan^6 theta=1+3 tan^2 th...

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

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

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